Answer: Emotion Engine chip

Context: Since the system's launch, production costs have been reduced significantly as a result of phasing out the Emotion Engine chip and falling hardware costs. The cost of manufacturing Cell microprocessors has fallen dramatically as a result of moving to the 65 nm production process, and Blu-ray Disc diodes have become cheaper to manufacture. As of January 2008, each unit cost around $400 to manufacture; by August 2009, Sony had reduced costs by a total of 70%, meaning it only costs Sony around $240 per unit.

Question: Along with a drop in the cost of hardware, PS3 has gotten cheaper to make because what chip was phased out?


Answer: Cell

Question: What's the name of the microprocessor produced by the 65 nm process?


Answer: diodes

Question: What specific component of Blu-Ray disc have also gotten less expensive to make?


Answer: $240

Question: As of Summer 2009, what was the cost to Sony to make a PS3?


Answer: 70%

Question: The August 2009 cost is a result of what percentage decrease in production cost?


Answer: 6/10

Context: Critical and commercial reception to PS3 improved over time, after a series of price revisions, Blu-ray's victory over HD DVD, and the release of several well received titles. Ars Technica's original launch review gave PS3 only a 6/10, but second review of the console in June 2008 rated it a 9/10. In September 2009, IGN named PlayStation 3 the 15th best gaming console of all time, behind both of its competitors: Wii (10th) and Xbox 360 (6th). However, PS3 has won IGN's "Console Showdown"—based on which console offers the best selection of games released during each year—in three of the four years since it began (2008, 2009 and 2011, with Xbox winning in 2010). IGN judged PlayStation 3 to have the best game line-up of 2008, based on their review scores in comparison to those of Wii and Xbox 360. In a comparison piece by PC mag's Will Greenwald in June 2012, PS3 was selected as an overall better console compared to Xbox 360. Pocket-lint said of the console "The PS3 has always been a brilliant games console," and that "For now, this is just about the best media device for the money."

Question: What rating did Ars Technica initially give PlayStation 3?


Answer: Xbox

Question: What PS3 competitor won IGN's "Console Showdown" in 2010?


Answer: Will Greenwald

Question: What PC Mag. staffer picked PS3 over Xbox in June, 2012?


Answer: Pocket-lint

Question: Which publication called the PlayStation 3 "a brilliant games console"?


Answer: 15th

Question: Where did IGN place the PS3 on their 2009 list of the best video game consoles ever?


Answer: "The Top 21 Tech Screwups of 2006"

Context: PS3 was given the number-eight spot on PC World magazine's list of "The Top 21 Tech Screwups of 2006", where it was criticized for being "Late, Expensive and Incompatible". GamesRadar ranked PS3 as the top item in a feature on game-related PR disasters, asking how Sony managed to "take one of the most anticipated game systems of all time and — within the space of a year — turn it into a hate object reviled by the entire internet", but added that despite its problems the system has "untapped potential". Business Week summed up the general opinion by stating that it was "more impressed with what [the PlayStation 3] could do than with what it currently does".

Question: What list by PC World ranked PlayStation eighth, in a bad way?


Answer: GamesRadar

Question: What gaming website called PS3 "a hate object reviled by the entire internet"?


Answer: "Late, Expensive and Incompatible"

Question: What quote sums up PC World's 2006 assessment of PS3?


Answer: a year

Question: How long did GamesRadar say it took Sony to turn the Internet against the PlayStation 3?


Answer: 2007

Context: Developers also found the machine difficult to program for. In 2007, Gabe Newell of Valve said "The PS3 is a total disaster on so many levels, I think it's really clear that Sony lost track of what customers and what developers wanted". He continued "I'd say, even at this late date, they should just cancel it and do a do over. Just say, 'This was a horrible disaster and we're sorry and we're going to stop selling this and stop trying to convince people to develop for it'". Doug Lombardi VP of Marketing for Valve has since stated that they are interested in developing for the console and are looking to hire talented PS3 programmers for future projects. He later restated Valve's position, "Until we have the ability to get a PS3 team together, until we find the people who want to come to Valve or who are at Valve who want to work on that, I don't really see us moving to that platform". At Sony's E3 2010 press conference, Newell made a live appearance to recant his previous statements, citing Sony's move to make the system more developer friendly, and to announce that Valve would be developing Portal 2 for the system. He also claimed that the inclusion of Steamworks (Valve's system to automatically update their software independently) would help to make the PS3 version of Portal 2 the best console version on the market.

Question: In what year did Gabe Newell call the PS3 "a total disaster"?


Answer: Doug Lombardi

Question: Who is Valve's VP of Marketing who says they want to hire programmers for a PS3 team?


Answer: 2010

Question: What year did Newell show up at Sony's EC3 press conference to take back what he said about PS3?


Answer: Portal 2

Question: What game did Valve develop for the PlayStation 3 console?


Answer: Steamworks

Question: What's the name of Valve's software update system?


Answer: developers

Context: Activision Blizzard CEO Bobby Kotick has criticized PS3's high development costs and inferior attach rate and return to that of Xbox 360 and Wii. He believes these factors are pushing developers away from working on the console. In an interview with The Times Kotick stated "I'm getting concerned about Sony; the PlayStation 3 is losing a bit of momentum and they don't make it easy for me to support the platform." He continued, "It's expensive to develop for the console, and the Wii and the Xbox are just selling better. Games generate a better return on invested capital (ROIC) on the Xbox than on the PlayStation." Kotick also claimed that Activision Blizzard may stop supporting the system if the situation is not addressed. "[Sony has] to cut the [PS3's retail] price, because if they don't, the attach rates are likely to slow. If we are being realistic, we might have to stop supporting Sony." Kotick received heavy criticism for the statement, notably from developer Bioware who questioned the wisdom of the threatened move, and referred to the statement as "silly."

Question: What group does Bobby Kotick think is being discouraged from working on the PS3?


Answer: return on invested capital

Question: What does "ROIC" stand for?


Answer: Activision Blizzard

Question: What company is Kotick the CEO of?


Answer: The Times

Question: What newspaper reported Kotick's concerns and his threat to stop supporting the PlayStation platform?


Answer: Bioware

Question: What game development company completely disagreed with Kotick's statements in The Times interview?


Answer: 8.8

Context: Despite the initial negative press, several websites have given the system very good reviews mostly regarding its hardware. CNET United Kingdom praised the system saying, "the PS3 is a versatile and impressive piece of home-entertainment equipment that lives up to the hype [...] the PS3 is well worth its hefty price tag." CNET awarded it a score of 8.8 out of 10 and voted it as its number one "must-have" gadget, praising its robust graphical capabilities and stylish exterior design while criticizing its limited selection of available games. In addition, both Home Theater Magazine and Ultimate AV have given the system's Blu-ray playback very favorable reviews, stating that the quality of playback exceeds that of many current standalone Blu-ray Disc players.

Question: What score did CNET give the PS3 out of ten?


Answer: Blu-ray playback

Question: What PlayStation 3 feature did Home Theater Magazine most like about PS3?


Answer: hardware

Question: Have reviews praised the PS3's hardware of software more frequently?


Answer: Ultimate AV

Question: What other reviewer agreed with Home Theater Magazine's assessment of the PS3's Blu-ray player?


Answer: CNET United Kingdom

Question: What website said the PlayStation 3 "lives up to the hype"?


Answer: Amazon.com

Context: The PlayStation 3 Slim received extremely positive reviews as well as a boost in sales; less than 24 hours after its announcement, PS3 Slim took the number-one bestseller spot on Amazon.com in the video games section for fifteen consecutive days. It regained the number-one position again one day later. PS3 Slim also received praise from PC World giving it a 90 out of 100 praising its new repackaging and the new value it brings at a lower price as well as praising its quietness and the reduction in its power consumption. This is in stark contrast to the original PS3's launch in which it was given position number-eight on their "The Top 21 Tech Screwups of 2006" list.

Question: With a day of its release, on what website did the PS3 Slim become the number-one bestseller?


Answer: fifteen

Question: For how many consecutive days did the PS3 Slim hold the number-one spot on Amazon.com?


Answer: 90 out of 100

Question: What score did the PS3 Slim earn from PC World?


Answer: PS3

Question: PC World's rave review of the PS3 Slim was a complete turnaround from their thoughts on what older model console?


Answer: repackaging

Question: Along with the PS Slim's value, quietness, and lower power usage, what superficial quality did PC World praise?


Answer: backward compatibility

Context: CNET awarded PS3 Slim four out of five stars praising its Blu-ray capabilities, 120 GB hard drive, free online gaming service and more affordable pricing point, but complained about the lack of backward compatibility for PlayStation 2 games. TechRadar gave PS3 Slim four and a half stars out of five praising its new smaller size and summed up its review stating "Over all, the PS3 Slim is a phenomenal piece of kit. It's amazing that something so small can do so much". However, they criticized the exterior design and the build quality in relation to the original model.

Question: What aspect of the PS3 Slim was CNET unhappy was missing for PS2 games?


Answer: four

Question: How many of five possible stars did CNET give the PS3 Slim?


Answer: four and a half

Question: How many of its own five stars did TechRadar award the PS3 Slim?


Answer: exterior

Question: What area of the console did TechRadar feel was designed poorly compared to the original PS3?


Answer: quietness

Context: The Super Slim model of PS3 has received positive reviews. Gaming website Spong praised the new Super Slim's quietness, stating "The most noticeable noise comes when the drive seeks a new area of the disc, such as when starting to load a game, and this occurs infrequently." They added that the fans are quieter than that of Slim, and went on to praise the new smaller, lighter size. Criticism was placed on the new disc loader, stating: "The cover can be moved by hand if you wish, there's also an eject button to do the work for you, but there is no software eject from the triangle button menus in the Xross Media Bar (XMB) interface. In addition, you have to close the cover by hand, which can be a bit fiddly if it's upright, and the PS3 won't start reading a disc unless you do [close the cover]." They also said there is no real drop in retail price.

Question: What quality of the PS3 Super Slim was the website Spong excited about?


Answer: smaller, lighter size

Question: In addition to quieter fans and drive, what change from the other models did Spong praise?


Answer: disc loader

Question: What piece of the PS3 Super Slim's hardware did Spong say was too "fiddly"?


Answer: close the cover

Question: What did Spong said you have to do to the disc loader before the console will start reading the disc?


Answer: CNET

Context: Tech media website CNET gave new Super Slim 4 out of 5 stars ("Excellent"), saying "The Super Slim PlayStation 3 shrinks a powerful gaming machine into an even tinier package while maintaining the same features as its predecessors: a great gaming library and a strong array of streaming services [...]", whilst also criticising the "cheap" design and disc-loader, stating: "Sometimes [the cover] doesn't catch and you feel like you're using one of those old credit card imprinter machines. In short, it feels cheap. You don't realize how convenient autoloading disc trays are until they're gone. Whether it was to cut costs or save space, this move is ultimately a step back." The criticism also was due to price, stating the cheapest Super Slim model was still more expensive than the cheapest Slim model, and that the smaller size and bigger hard drive shouldn't be considered an upgrade when the hard drive on a Slim model is easily removed and replaced. They did praise that the hard drive of the Super Slim model is "the easiest yet. Simply sliding off the side panel reveals the drive bay, which can quickly be unscrewed." They also stated that whilst the Super Slim model is not in any way an upgrade, it could be an indicator as to what's to come. "It may not be revolutionary, but the Super Slim PS3 is the same impressive machine in a much smaller package. There doesn't seem to be any reason for existing PS3 owners to upgrade, but for the prospective PS3 buyer, the Super Slim is probably the way to go if you can deal with not having a slot-loading disc drive."

Question: What website rated the Super Slim four out of five stars?


Answer: "cheap"

Question: What adjective did CNET use to describe the PS3 Super Slim's design?


Answer: hard drive

Question: What component of the Super Slim did CNET call "the easiest yet"?


Answer: disc-loader

Question: What hardware component did CNET have the biggest problem with, even comparing it to an old credit card reader?


Answer: more expensive

Question: Was the lowest-priced Super Slim more or less expensive than any of the PS3 Slim models?


Answer: T3

Context: Technology magazine T3 gave the Super Slim model a positive review, stating the console is almost "nostalgic" in the design similarities to the original "fat" model, "While we don’t know whether it will play PS3 games or Blu-ray discs any differently yet, the look and feel of the new PS3 Slim is an obvious homage to the original PS3, minus the considerable excess weight. Immediately we would be concerned about the durability of the top loading tray that feels like it could be yanked straight out off the console, but ultimately it all feels like Sony's nostalgic way of signing off the current generation console in anticipation for the PS4."

Question: What magazine described the Super Slim as "nostalgic"?


Answer: the original PS3

Question: What PlayStation 3 model did T3 feel the Super Slim's design was paying homage to?


Answer: weight

Question: According to T3, what was the main differentiator between the "fat" PS3 and the Super Slim?


Answer: the top loading tray

Question: What hardware element did T3 feel might have issues with durability?


Answer: the PS4

Question: T3 felt Sony was saying goodbye to past models in preparation for what next-generation console?


Answer: House of Lords

Context: Royal assent is sometimes associated with elaborate ceremonies. In the United Kingdom, for instance, the sovereign may appear personally in the House of Lords or may appoint Lords Commissioners, who announce that royal assent has been granted at a ceremony held at the Palace of Westminster. However, royal assent is usually granted less ceremonially by letters patent. In other nations, such as Australia, the governor-general merely signs the bill. In Canada, the governor general may give assent either in person at a ceremony held in the Senate or by a written declaration notifying parliament of his or her agreement to the bill.

Question: When royal assent takes place in the UK, where does the sovereign make an appearance?


Answer: Palace of Westminster

Question: Alternatively, when UK Lord Commissioners take the sovereign's place in the ceremony, where does the ceremony take place?


Answer: written declaration

Question: Canadian governor generals can give their assent in person or by which other method?


Answer: elaborate ceremonies

Question: With what is royal assent sometimes associated with?


Answer: Palace of Westminster

Question: Where is a royal assent ceremony held within the United Kingdom?


Answer: letters patent

Question: With what method is royal assent generally granted?


Answer: the governor-general merely signs the bill

Question: How is royal assent granted within Australia?


Answer: constitutional monarch

Context: Royal assent is the method by which a country's constitutional monarch (possibly through a delegated official) formally approves an act of that nation's parliament, thus making it a law or letting it be promulgated as law. In the vast majority of contemporary monarchies, this act is considered to be little more than a formality; even in those nations which still permit their ruler to withhold the royal assent (such as the United Kingdom, Norway, and Liechtenstein), the monarch almost never does so, save in a dire political emergency or upon the advice of their government. While the power to withhold royal assent was once exercised often in European monarchies, it is exceedingly rare in the modern, democratic political atmosphere that has developed there since the 18th century.

Question: Royal assent is a process of approving a nation's legislative acts by whom?


Answer: United Kingdom, Norway, and Liechtenstein

Question: Which three modern monarchies allow their ruler to withhold royal assent?


Answer: 18th

Question: Since which century have modern political processes forgone royal assent?


Answer: United Kingdom, Norway, and Liechtenstein

Question: What nations allow the withold of the royal assent?


Answer: a dire political emergency or upon the advice of their government

Question: Under what circumstances does a monarch typically use the royal assent?


Answer: exceedingly rare

Question: Is usage of the royal assent frequent or rare in today's societies?


Answer: ministers

Context: Under modern constitutional conventions, the sovereign acts on the advice of his or her ministers. Since these ministers most often maintain the support of parliament and are the ones who obtain the passage of bills, it is highly improbable that they would advise the sovereign to withhold assent. An exception is sometimes stated to be if bills are not passed in good faith, though it is difficult to make an interpretation on what this circumstance might constitute. Hence, in modern practice, royal assent is always granted; a refusal to do so would be appropriate only in an emergency requiring the use of the monarch's reserve powers.

Question: Modern-day sovereigns often acts on the advice of whom?


Answer: reserve powers

Question: In the event that the monarch refuses to give royal assent, what can the monarch make use of?


Answer: his or her ministers

Question: Whose advice does a sovereign follow?


Answer: ministers

Question: Who often maintains parliamentary support and obtains the passage of bills?


Answer: improbable

Question: Is it probable, improbable, or impossible that a sovereign would withhold assent?


Answer: Royal Council

Context: Originally, legislative power was exercised by the sovereign acting on the advice of the Curia Regis, or Royal Council, in which important magnates and clerics participated and which evolved into parliament. The so-called Model Parliament included bishops, abbots, earls, barons, and two knights from each shire and two burgesses from each borough among its members. In 1265, the Earl of Leicester irregularly called a full parliament without royal authorisation. The body eventually came to be divided into two branches: bishops, abbots, earls, and barons formed the House of Lords, while the shire and borough representatives formed the House of Commons. The King would seek the advice and consent of both houses before making any law. During Henry VI's reign, it became regular practice for the two houses to originate legislation in the form of bills, which would not become law unless the sovereign's assent was obtained, as the sovereign was, and still remains, the enactor of laws. Hence, all acts include the clause "Be it enacted by the Queen's (King's) most Excellent Majesty, by and with the advice and consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the authority of the same, as follows...". The Parliament Acts 1911 and 1949 provide a second potential preamble if the House of Lords were to be excluded from the process.

Question: What is another name for "Curia Regis"?


Answer: Earl of Leicester

Question: Who was it that peculiarly called a full parliament without royal authorization in 1265?


Answer: House of Lords

Question: As a result, the bishops, abbots, earls, and barons formed which body of parliament?


Answer: House of Commons

Question: Which body did the shire and borough representatives form?


Answer: Curia Regis, or Royal Council

Question: From what did parliament evolve?


Answer: bishops, abbots, earls, and barons

Question: What positions were contained within the House of Lords?


Answer: House of Commons

Question: Which branch of parliament contains shire and borough representatives?


Answer: the sovereign

Question: A bill could not become a law without whose assent?


Answer: the sovereign

Question: Who is considered the enactor of laws?


Answer: Charles I

Context: The power of parliament to pass bills was often thwarted by monarchs. Charles I dissolved parliament in 1629, after it passed motions critical of and bills seeking to restrict his arbitrary exercise of power. During the eleven years of personal rule that followed, Charles performed legally dubious actions, such as raising taxes without parliament's approval. After the English Civil War, it was accepted that parliament should be summoned to meet regularly, but it was still commonplace for monarchs to refuse royal assent to bills. In 1678, Charles II withheld his assent from a bill "for preserving the Peace of the Kingdom by raising the Militia, and continuing them in Duty for Two and Forty Days," suggesting that he, not parliament, should control the militia. The last Stuart monarch, Anne, similarly withheld on 11 March 1708, on the advice of her ministers, her assent from a bill for the settling of Militia in Scotland. No monarch has since withheld royal assent on a bill passed by the British parliament.

Question: Which monarch was responsible for dissolving parliament in 1629?


Answer: raising taxes

Question: What is one action this monarch took that is typically left to the discretion of parliament?


Answer: English Civil War

Question: After which event was it decided that parliament should meet on a regular basis?


Answer: Anne

Question: Like Charles II had previously done, the last Stuart monarch withheld assent. Who was this monarch?


Answer: Charles I

Question: Which ruler removed parliament in 1629?


Answer: her ministers

Question: Under whose advice did Anne withold the royal assent?


Answer: restrict his arbitrary exercise of power

Question: What did motions attempt to accomplish that prompted Charles I to dissolve parliament in 1629?


Answer: 11 March 1708

Question: When was the last time royal assent was enacted?


Answer: Anne

Question: Who was the last monarch to use the royal assent in 1708?


Answer: Hanoverian dynasty

Context: During the rule of the succeeding Hanoverian dynasty, power was gradually exercised more by parliament and the government. The first Hanoverian monarch, George I, relied on his ministers to a greater extent than did previous monarchs. Later Hanoverian monarchs attempted to restore royal control over legislation: George III and George IV both openly opposed Catholic Emancipation and asserted that to grant assent to a Catholic emancipation bill would violate the Coronation Oath, which required the sovereign to preserve and protect the established Church of England from Papal domination and would grant rights to individuals who were in league with a foreign power which did not recognise their legitimacy. However, George IV reluctantly granted his assent upon the advice of his ministers. Thus, as the concept of ministerial responsibility has evolved, the power to withhold royal assent has fallen into disuse, both in the United Kingdom and in the other Commonwealth realms.

Question: During whose rule was power transferred more to parliament?


Answer: George I

Question: Who was the first ruler during this dynasty?


Answer: Catholic Emancipation

Question: In attempting to take back control, George III and George IV opposed which church movement?


Answer: George I

Question: Which monarch relied on his ministers more than any of his predecessors?


Answer: Catholic Emancipation

Question: What did George III and George IV both oppose?


Answer: Coronation Oath

Question: What rule did George III and George IV believe a Catholic emancipation bill would violate?


Answer: George IV

Question: Which monarch granted assent reluctantly under the advise of his ministers?


Answer: Presiding Officer of the Scottish Parliament

Context: Royal assent is the final stage in the legislative process for acts of the Scottish parliament. The process is governed by sections 28, 32, and 33 of the Scotland Act 1998. After a bill has been passed, the Presiding Officer of the Scottish Parliament submits it to the monarch for royal assent after a four-week period, during which the Advocate General for Scotland, the Lord Advocate, the Attorney General or the Secretary of State for Scotland may refer the bill to the Supreme Court of the United Kingdom (prior to 1 October 2009, the Judicial Committee of the Privy Council) for review of its legality. Royal assent is signified by letters patent under the Great Seal of Scotland in the following form which is set out in The Scottish Parliament (Letters Patent and Proclamations) Order 1999 (SI 1999/737) and of which notice is published in the London, Edinburgh, and Belfast Gazettes:

Question: In Scotland, who is responsible for submitting a bill for royal assent?


Answer: London, Edinburgh, and Belfast Gazettes

Question: Which three publications are used to signify royal assent?


Answer: 28, 32, and 33

Question: Under which Scotland Act sections is the royal assent governed?


Answer: four-week period

Question: How many weeks pass before the monarch receives a bill from the Presiding Officer?


Answer: Advocate General for Scotland, the Lord Advocate, the Attorney General or the Secretary of State

Question: Which entities have the capability to refer a bill to the Supreme Court?


Answer: review of its legality

Question: For what would a bill be submitted to the Supreme Court of Scotland?


Answer: Measures

Context: Measures, which were the means by which the National Assembly for Wales passed legislation between 2006 and 2011, were assented to by the Queen by means of an Order in Council. Section 102 of the Government of Wales Act 2006 required the Clerk to the Assembly to present measures passed by the assembly after a four-week period during which the Counsel General for Wales or the Attorney General could refer the proposed measure to the Supreme Court for a decision as to whether the measure was within the assembly's legislative competence.

Question: What was the name of the method by which Wales passed legislation in the 2000's?


Answer: Counsel General for Wales or the Attorney General

Question: After a four-week period, who could refer a proposed measure to the Supreme Court?


Answer: the means by which the National Assembly for Wales passed legislation between 2006 and 2011

Question: What were "measures" in Wales?


Answer: 2006 and 2011

Question: During which years were measures used in order to pass legislation in Wales?


Answer: Counsel General for Wales or the Attorney General

Question: In Wales, who had the capability of submitting a bill to the Supreme Court?


Answer: Order in Council

Context: Instead, the monarch directly grants royal assent by Order in Council. Assent is granted or refused on the advice of the Lord Chancellor. A recent example when assent was refused (or, more correctly, when the Lord Chancellor declined to present the law for assent) was in 2007, concerning reforms to the constitution of the Chief Pleas of Sark. (A revised version of the proposed reforms was subsequently given assent.) In 2011, campaigners against a law that sought to reduce the number of senators in the states of Jersey petitioned the Privy Council to advise the Queen to refuse royal assent. An Order in Council of 13 July 2011 established new rules for the consideration of petitions against granting royal assent.

Question: The sovereign grants assent by which order?


Answer: Lord Chancellor

Question: Who advises the sovereign in this decision?


Answer: Chief Pleas of Sark

Question: Which recent petition for reforms to the constitution led to assent being refused?


Answer: Lord Chancellor

Question: Who advises a bill to be granted or refused?


Answer: 13 July 2011

Question: When was an Order in Counil passed that laid out new rules for consideration of petitions against the royal assent?


Answer: 2007

Question: In what year did the Lord Chancellor refuse to present a law concerning constituational reform for assent?


Answer: reforms to the constitution of the Chief Pleas of Sark

Question: What was the subject of the bill that the Lord Chancellor refused to present for royal assent in 2007?


Answer: Tynwald Hill at St John's

Context: Royal assent is not sufficient to give legal effect to an Act of Tynwald. By ancient custom, an act did not come into force until it had been promulgated at an open-air sitting of Tynwald, usually held on Tynwald Hill at St John's on St John's Day (24 June), but, since the adoption of the Gregorian calendar in 1753, on 5 July (or on the following Monday if 5 July is a Saturday or Sunday). Promulgation originally consisted of the reading of the Act in English and Manx; but, after 1865 the reading of the title of the act and a summary of each section were sufficient. This was reduced in 1895 to the titles and a memorandum of the object and purport of the act, and, since 1988, only the short title and a summary of the long title have been read.

Question: Under ancient custom, an Act of Tynwald didn't go into effect until decreed at which location?


Answer: Manx

Question: Promulgation of an Act of Tynwald originally consisted of reading it in English and which other language?


Answer: summary of the long title

Question: Nowadays, only the short title and what else are read?


Answer: only the short title and a summary of the long title

Question: How much of the proposed act must be currently read aloud on St John's Day?


Answer: (24 June)

Question: On what day does St John's Day occur?


Answer: Tynwald Hill at St John's

Question: Where is the open-air sitting of Tynwald usually held?


Answer: Sodor and Man Diocesan Synod

Context: Since 1993, the Sodor and Man Diocesan Synod has had power to enact measures making provision "with respect to any matter concerning the Church of England in the Island". If approved by Tynwald, a measure "shall have the force and effect of an Act of Tynwald upon the Royal Assent thereto being announced to Tynwald". Between 1979 and 1993, the Synod had similar powers, but limited to the extension to the Isle of Man of measures of the General Synod. Before 1994, royal assent was granted by Order in Council, as for a bill, but the power to grant royal assent to measures has now been delegated to the lieutenant governor. A Measure does not require promulgation.

Question: Since 1993, which body has had power to enact measures?


Answer: Church of England in the Island

Question: This body makes provisions in respect to matters concerning whom?


Answer: Order in Council

Question: Up until 1994, royal assent was given by whom?


Answer: lieutenant governor

Question: Which position now has the power to grant royal assent?


Answer: 1994

Question: Before what year was royal assent approved by Order in Council?


Answer: the lieutenant governor

Question: Who currently holds the power to grant royal assent to measures?


Answer: Between 1979 and 1993

Question: During which years did the Synod have power to enact measures?


Answer: the Governor General of Canada

Context: If the Governor General of Canada is unable to give assent, it can be done by either the Deputy of the Governor General of Canada—the Chief Justice of Canada—or another justice of the Supreme Court of Canada. It is not actually necessary for the governor general to sign a bill passed by a legislature, the signature being merely an attestation. In each case, the parliament must be apprised of the granting of assent before the bill is considered to have become law. Two methods are available: the sovereign's representatives may grant assent in the presence of both houses of parliament; alternatively, each house may be notified separately, usually by the speaker of that house. However, though both houses must be notified on the same day, notice to the House of Commons while it is not in session may be given by way of publishing a special issue of the Journals of the House of Commons, whereas the Senate must be sitting and the governor general's letter read aloud by the speaker.

Question: In the Canadian federal government, who is typically responsible for deciding wether to give assent?


Answer: Chief Justice of Canada—or another justice

Question: Which positions from the Canadian Supreme Court may also give assent if need be?


Answer: the Deputy of the Governor General of Canada—the Chief Justice of Canada—or another justice of the Supreme Court of Canada

Question: Who has the capability of granting assent if the Governer General of Canada cannot?


Answer: Two

Question: How many methods are available to grant assent in Canada?


Answer: both houses must be notified on the same day

Question: If each house of parliament is notified seperately, what regulation applies?


Answer: publishing a special issue of the Journals of the House of Commons

Question: How can the House of Commons be notified of assent if it is not in session?


Answer: governor general's letter read aloud by the speaker

Question: In contrast to the House of Commons, how must the Senate be notified of assent?


Answer: 1708

Context: While royal assent has not been withheld in the United Kingdom since 1708, it has often been withheld in British colonies and former colonies by governors acting on royal instructions. In the United States Declaration of Independence, colonists complained that George III "has refused his Assent to Laws, the most wholesome and necessary for the public good [and] has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them." Even after colonies such as Canada, Australia, New Zealand, the Union of South Africa, and Newfoundland were granted responsible government, the British government continued to sometimes advise governors-general on the granting of assent; assent was also occasionally reserved to allow the British government to examine a bill before advising the governor-general.

Question: Which year was royal assent last withheld in the UK?


Answer: George III

Question: The United States Declaration of Independence mentions which British monarch?


Answer: refused his Assent to Laws

Question: What did the American colonies accuse the monarch of?


Answer: 1708

Question: In what year was royal assent last witheld in the UK?


Answer: the British government

Question: Who continued to advise governors-general of granting of assent, even after their colonies had responsible government?


Answer: colonies such as Canada, Australia, New Zealand, the Union of South Africa, and Newfoundland

Question: To whom did the British government occasionally still advice on the royal assent, although they had their own responsible governments?


Answer: Governor-General

Context: In Australia, a technical issue arose with the royal assent in both 1976 and 2001. In 1976, a bill originating in the House of Representatives was mistakenly submitted to the Governor-General and assented to. However, it was later discovered that it had not been passed by each house. The error arose because two bills of the same title had originated from the house. The Governor-General revoked the first assent, before assenting to the bill which had actually passed. The same procedure was followed to correct a similar error which arose in 2001.

Question: The bill from the Australian House of Representatives was mistakenly sent and assented to by whom in 1976?


Answer: two bills of the same title had originated from the house

Question: Why did this occur?


Answer: revoked the first assent

Question: What did the Governor-General do with the first assent?


Answer: 2001

Question: This same procedure was more recently done to fix a similar error in which year?


Answer: two bills of the same title had originated from the house

Question: What was the reason a bill was accidentally assented in 1976?


Answer: 2001

Question: After an accidental assention of a bill with same name in 1976, when did a similar mistaken assention occur in Australia?


Answer: it had not been passed by each house

Question: What protocol was not followed in 1976 when a bill was mistakenly assented?


Answer: The Governor-General revoked the first assent, before assenting to the bill which had actually passed

Question: How was the case of two bills mistakenly assented corrected both in 1796 and 2001?


Answer: Tynwald

Context: Special procedures apply to legislation passed by Tynwald, the legislature of the Isle of Man. Before the lordship of the Island was purchased by the British Crown in 1765 (the Revestment), the assent of the Lord of Mann to a bill was signified by letter to the governor. After 1765, royal assent was at first signified by letter from the Secretary of State to the governor; but, during the British Regency, the practice began of granting royal assent by Order in Council, which continues to this day, though limited to exceptional cases since 1981.

Question: What term refers to the legislature of the Isle of man?


Answer: 1765

Question: In what year was lordship of the Isle of Man purchased?


Answer: lordship of the Island was purchased by the British Crown in 1765

Question: What does the term the Revestment refer to?


Answer: by letter from the Secretary of State to the governor

Question: Previous to the Order in Council method, how was royal assent passed previously within the Isle of Man?


Answer: Order in Council

Question: How is royal assent currently granted in the Isle of Man?


Answer: the governor-general

Context: In Commonwealth realms other than the UK, royal assent is granted or withheld either by the realm's sovereign or, more frequently, by the representative of the sovereign, the governor-general. In federated realms, assent in each state, province, or territory is granted or withheld by the representatives of the sovereign. In Australia, this is the governors of the states, administrators of the territories, or the governor-general in the Australian Capital Territory. For Canada, this is the lieutenant governors of the provinces. A lieutenant governor may defer assent to the governor general, and the governor general may defer assent to federal bills to the sovereign.

Question: In Commonwealth realms, who is the representative of the sovereign?


Answer: lieutenant governors of the provinces

Question: Who grants royal assent in Canada?


Answer: A lieutenant governor may defer assent to the governor general, and the governor general may defer assent to federal bills to the sovereign.

Question: In Canada, who is authorized to defer assent and to whom?


Answer: by the realm's sovereign or, more frequently, by the representative of the sovereign

Question: Who grants the royal assent in Commonwealth nations other than the UK?


Answer: Balfour Declaration of 1926 and the Statute of Westminster 1931

Context: Since the Balfour Declaration of 1926 and the Statute of Westminster 1931, the all Commonwealth realms have been sovereign kingdoms, the monarch and governors-general acting solely on the advice of the local ministers who generally maintain the support of the legislature and are the ones who secure the passage of bills. They, therefore, are unlikely to advise the sovereign or his or her representative to withhold assent. The power to withhold the royal assent was exercised by Alberta's lieutenant governor, John C. Bowen, in 1937, in respect of three bills passed in the legislature dominated by William Aberhart's Social Credit party. Two bills sought to put banks under the authority of the province, thereby interfering with the federal government's powers. The third, the Accurate News and Information Bill, purported to force newspapers to print government rebuttals to stories to which the provincial cabinet objected. The unconstitutionality of all three bills was later confirmed by the Supreme Court of Canada and by the Judicial Committee of the Privy Council.

Question: What two documents declared all Commonwealth realms as sovereign kingdoms?


Answer: John C. Bowen

Question: Who exercised the power to withold royal assent in Alberta in 1937?


Answer: force newspapers to print government rebuttals to stories to which the provincial cabinet objected

Question: What the did Accurate News and Information Bill hope to accomplish?


Answer: Supreme Court of Canada and by the Judicial Committee of the Privy Council.

Question: Who decided the unconstitutionality of three bills brought forth by the Social Credit party?


Answer: House of Commons and the House of Lords

Context: In the United Kingdom, a bill is presented for royal assent after it has passed all the required stages in both the House of Commons and the House of Lords. Under the Parliament Acts 1911 and 1949, the House of Commons may, under certain circumstances, direct that a bill be presented for assent despite lack of passage by the House of Lords. Officially, assent is granted by the sovereign or by Lords Commissioners authorised to act by letters patent. It may be granted in parliament or outside parliament; in the latter case, each house must be separately notified before the bill takes effect.

Question: Which Houses in the UK must approve a bill before it is assented?


Answer: Parliament Acts 1911 and 1949

Question: Which Parliamentary Acts allow a bill to be presented for assent even after the House of Lords has refused it?


Answer: the sovereign or by Lords Commissioners

Question: Who can be authorized to grant assent by letters patent?


Answer: Anglo-Norman Law French

Context: The Clerk of the Parliaments, an official of the House of Lords, traditionally states a formula in Anglo-Norman Law French, indicating the sovereign's decision. The granting of royal assent to a supply bill is indicated with the words "La Reyne remercie ses bons sujets, accepte leur benevolence, et ainsi le veult", translated as "The Queen thanks her good subjects, accepts their bounty, and wills it so." For other public or private bills, the formula is simply "La Reyne le veult" ("the Queen wills it"). For personal bills, the phrase is "Soit fait comme il est désiré" ("let it be as it is desired"). The appropriate formula for withholding assent is the euphemistic "La Reyne s'avisera" ("the Queen will consider it"). When the sovereign is male, Le Roy is substituted for La Reyne.

Question: In what language does the Clerk of the Parliaments announce Parliament's decision?


Answer: "La Reyne remercie ses bons sujets, accepte leur benevolence, et ainsi le veult"

Question: What words in Anglo-Norman Law French announce a granted assent?


Answer: "La Reyne le veult"

Question: What is the shortened version of the notification of assent?


Answer: "La Reyne s'avisera"

Question: What phrase is used to announce a withheld assent?


Answer: The Clerk of the Crown

Context: Before the reign of Henry VIII, the sovereign always granted his or her assent in person. The sovereign, wearing the Imperial State Crown, would be seated on the throne in the Lords chamber, surrounded by heralds and members of the royal court—a scene that nowadays is repeated only at the annual State Opening of Parliament. The Commons, led by their speaker, would listen from the Bar of the Lords, just outside the chamber. The Clerk of the Parliaments presented the bills awaiting assent to the monarch, save that supply bills were traditionally brought up by the speaker. The Clerk of the Crown, standing on the sovereign's right, then read aloud the titles of the bills (in earlier times, the entire text of the bills). The Clerk of the Parliaments, standing on the sovereign's left, responded by stating the appropriate Norman French formula.

Question: When assention was formally granted in person, who read the titles of the bills?


Answer: stating the appropriate Norman French formula

Question: What job did the Clerk of the Parliaments have during assention notifications?


Answer: Henry VIII

Question: Before whose reign was assent always granted in person?


Answer: the annual State Opening of Parliament

Question: Nowadays, when is the only time a formal assention ceremony occurs?


Answer: right

Question: On which side of the soverign does the Clerk of the Crown stand?


Answer: committing adultery

Context: A new device for granting assent was created during the reign of King Henry VIII. In 1542, Henry sought to execute his fifth wife, Catherine Howard, whom he accused of committing adultery; the execution was to be authorised not after a trial but by a bill of attainder, to which he would have to personally assent after listening to the entire text. Henry decided that "the repetition of so grievous a Story and the recital of so infamous a crime" in his presence "might reopen a Wound already closing in the Royal Bosom". Therefore, parliament inserted a clause into the Act of Attainder, providing that assent granted by Commissioners "is and ever was and ever shall be, as good" as assent granted by the sovereign personally. The procedure was used only five times during the 16th century, but more often during the 17th and 18th centuries, especially when George III's health began to deteriorate. Queen Victoria became the last monarch to personally grant assent in 1854.

Question: Why did Henry VIII wish to execute his fifth wife?


Answer: listening to the entire text

Question: What was Henry VIII trying to avoid by creating a new procedure for granting assent?


Answer: five

Question: How many times in the 16th century was assent granted by Commissioners?


Answer: Queen Victoria

Question: Who was the last monarch to grant assent personally?


Answer: five

Context: When granting assent by commission, the sovereign authorises three or more (normally five) lords who are Privy Counsellors to grant assent in his or her name. The Lords Commissioners, as the monarch's representatives are known, wear scarlet parliamentary robes and sit on a bench between the throne and the Woolsack. The Lords Reading Clerk reads the commission aloud; the senior commissioner then states, "My Lords, in obedience to Her Majesty's Commands, and by virtue of the Commission which has been now read, We do declare and notify to you, the Lords Spiritual and Temporal and Commons in Parliament assembled, that Her Majesty has given Her Royal Assent to the several Acts in the Commission mentioned."

Question: How many lords are usually present during assent by Commissioner?


Answer: scarlet parliamentary robes

Question: What do the Lords Commissioners wear to a ceremony of assent?


Answer: the senior

Question: Which commissioner reads the formal closing statement to the assention ceremony?


Answer: The Lords Reading Clerk

Question: Which position reads the commisssion aloud during tthe ceremony?


Answer: the 1960s

Context: During the 1960s, the ceremony of assenting by commission was discontinued and is now only employed once a year, at the end of the annual parliamentary session. In 1960, the Gentleman Usher of the Black Rod arrived to summon the House of Commons during a heated debate and several members protested against the disruption by refusing to attend the ceremony. The debacle was repeated in 1965; this time, when the Speaker left the chair to go to the House of Lords, some members continued to make speeches. As a result, the Royal Assent Act 1967 was passed, creating an additional form for the granting of royal assent. As the attorney-general explained, "there has been a good deal of resentment not only at the loss of Parliamentary time that has been involved but at the breaking of the thread of a possibly eloquent speech and the disruption of a debate that may be caused." The granting of assent by the monarch in person, or by commission, is still possible, but this third form is used on a day-to-day basis.

Question: During which decade was assention by commission discontinued?


Answer: once a year, at the end of the annual parliamentary session

Question: When does assention by commission occur today?


Answer: 1960

Question: In whatear did several members refuse to attend the assention ceremony after a heated debate?


Answer: Royal Assent Act 1967

Question: What was passed in reference to the discord in 1960 and 1965 during assention cremonies?


Answer: does not require both houses to meet jointly

Context: Under the Royal Assent Act 1967, royal assent can be granted by the sovereign in writing, by means of letters patent, that are presented to the presiding officer of each house of parliament. Then, the presiding officer makes a formal, but simple statement to the house, acquainting each house that royal assent has been granted to the acts mentioned. Thus, unlike the granting of royal assent by the monarch in person or by Royal Commissioners, the method created by the Royal Assent Act 1967 does not require both houses to meet jointly for the purpose of receiving the notice of royal assent. The standard text of the letters patent is set out in The Crown Office (Forms and Proclamations Rules) Order 1992, with minor amendments in 2000. In practice this remains the standard method, a fact that is belied by the wording of the letters patent for the appointment of the Royal Commissioners and by the wording of the letters patent for the granting of royal assent in writing under the 1967 Act ("... And forasmuch as We cannot at this time be present in the Higher House of Our said Parliament being the accustomed place for giving Our Royal Assent...").

Question: What is unique about the method used for assention allowed by the Royal Assent Act 1967?


Answer: by the sovereign in writing, by means of letters patent, that are presented to the presiding officer of each house of parliament

Question: How is assent granted under the Royal Assent Act 1967?


Answer: The Crown Office (Forms and Proclamations Rules) Order 1992

Question: Which document formats the letters patent?


Answer: 2000

Question: In which year were minor amendments made to the Crown Office Order?


Answer: when the assent is declared in the presence of both houses jointly assembled

Context: When the act is assented to by the sovereign in person, or by empowered Royal Commissioners, royal assent is considered given at the moment when the assent is declared in the presence of both houses jointly assembled. When the procedure created by the Royal Assent Act 1967 is followed, assent is considered granted when the presiding officers of both houses, having received the letters patent from the king or queen signifying the assent, have notified their respective house of the grant of royal assent. Thus, if each presiding officer makes the announcement at a different time (for instance because one house is not sitting on a certain date), assent is regarded as effective when the second announcement is made. This is important because, under British Law, unless there is any provision to the contrary, an act takes effect on the date on which it receives royal assent and that date is not regarded as being the date when the letters patent are signed, or when they are delivered to the presiding officers of each house, but the date on which both houses have been formally acquainted of the assent.

Question: When assent is granted in person, when is it formally considered final?


Answer: notified their respective house of the grant of royal assent

Question: An assent is considered granted when applying the Royal Assent Act 1967 when both presiding officers have done what?


Answer: when the second announcement is made

Question: When is assent effective if the presiding officers inform their houses at different times?


Answer: Clerk of the Parliaments

Context: Independently of the method used to signify royal assent, it is the responsibility of the Clerk of the Parliaments, once the assent has been duly notified to both houses, not only to endorse the act in the name of the monarch with the formal Norman French formula, but to certify that assent has been granted. The clerk signs one authentic copy of the bill and inserts the date (in English) on which the assent was notified to the two houses after the title of the act. When an act is published, the signature of the clerk is omitted, as is the Norman French formula, should the endorsement have been made in writing. However, the date on which the assent was notified is printed in brackets.

Question: Whose responsibility is it to assure that assent has been granted?


Answer: signature of the clerk is omitted, as is the Norman French formula

Question: What is omitted when an act is published?


Answer: Clerk of the Parliaments

Question: Who writes the formal Norman French formula on passed acts?


Answer: 1875

Context: In Australia, the formal ceremony of granting assent in parliament has not been regularly used since the early 20th century. Now, the bill is sent to the governor-general's residence by the house in which it originated. The governor-general then signs the bill, sending messages to the President of the Senate and the Speaker of the House of Representatives, who notify their respective houses of the governor-general's action. A similar practice is followed in New Zealand, where the governor-general has not personally granted the Royal Assent in parliament since 1875.

Question: In what year did the New Zealand governor-general last personally grant the royal assent in parliament?


Answer: Australia

Question: Which country has not used the formal assention ceremony since the early 20th century?


Answer: President of the Senate and the Speaker of the House of Representatives

Question: Who are the leaders of each house given the responsibility of informing their group of the governor-generals actions?


Answer: the 21st century

Context: In Canada, the traditional ceremony for granting assent in parliament was regularly used until the 21st century, long after it had been discontinued in the United Kingdom and other Commonwealth realms. One result, conceived as part of a string of royal duties intended to demonstrate Canada's status as an independent kingdom, was that King George VI personally assented to nine bills of the Canadian parliament during the 1939 royal tour of Canada—85 years after his great-grandmother, Queen Victoria, had last granted royal assent personally in the United Kingdom. Under the Royal Assent Act 2002, however, the alternative practice of granting assent in writing, with each house being notified separately ( the Speaker of the Senate or a representative reads to the senators the letters from the governor general regarding the written declaration of Royal Assent), was brought into force. As the act also provides, royal assent is to be signified—by the governor general, or, more often, by a deputy, usually a Justice of the Supreme Court, at least twice each calendar year: for the first appropriation measure and for at least one other act, usually the first non-appropriation measure passed. However, the act provides that a grant of royal assent is not rendered invalid by a failure to employ the traditional ceremony where required.

Question: When did Canada finally cease to use the traditional ceremony for granting assent as regular practice?


Answer: 85 years after his great-grandmother, Queen Victoria, had last granted royal assent personally

Question: Why was King George VI's personal assent in 1939 noteworthy?


Answer: Royal Assent Act 2002

Question: With what bill in Canada did granting assent by writing become effective?


Answer: House of Commons

Context: The Royal Assent ceremony takes place in the Senate, as the sovereign is traditionally barred from the House of Commons. On the day of the event, the Speaker of the Senate will read to the chamber a notice from the secretary to the governor general indicating when the viceroy or a deputy thereof will arrive. The Senate thereafter cannot adjourn until after the ceremony. The speaker moves to sit beside the throne, the Mace Bearer, with mace in hand, stands adjacent to him or her, and the governor general enters to take the speaker's chair. The Usher of the Black Rod is then commanded by the speaker to summon the Members of Parliament, who follow Black Rod back to the Senate, the Sergeant-at-Arms carrying the mace of the House of Commons. In the Senate, those from the commons stand behind the bar, while Black Rod proceeds to stand next to the governor general, who then nods his or her head to signify Royal Assent to the presented bills (which do not include appropriations bills). Once the list of bills is complete, the Clerk of the Senate states: "in Her Majesty's name, His [or Her] Excellency the Governor General [or the deputy] doth assent to these bills." If there are any appropriation bills to receive Royal Assent, the Speaker of the House of Commons will read their titles and the Senate clerk repeats them to the governor general, who nods his or her head to communicate Royal Assent. When these bills have all been assented to, the Clerk of the Senate recites "in Her Majesty's name, His [or Her] Excellency the Governor General [or the deputy] thanks her loyal subjects, accepts their benevolence and assents to these bills. The governor general or his or her deputy then depart parliament.

Question: From where is the sovereign typically forbidden?


Answer: The governor general or his or her deputy

Question: Whose job is it to release parliament after the ceremony?


Answer: Clerk of the Senate

Question: Who reads the formal statement after the list of bills has been finished?


Answer: governor general

Question: Which position nods their head to signify assention?


Answer: sanction royale

Context: In Belgium, the sanction royale has the same legal effect as royal assent; the Belgian constitution requires a theoretically possible refusal of royal sanction to be countersigned—as any other act of the monarch—by a minister responsible before the House of Representatives. The monarch promulgates the law, meaning that he or she formally orders that the law be officially published and executed. In 1990, when King Baudouin advised his cabinet he could not, in conscience, sign a bill decriminalising abortion (a refusal patently not covered by a responsible minister), the Council of Ministers, at the King's own request, declared Baudouin incapable of exercising his powers. In accordance with the Belgian constitution, upon the declaration of the sovereign's incapacity, the Council of Ministers assumed the powers of the head of state until parliament could rule on the King's incapacity and appoint a regent. The bill was then assented to by all members of the Council of Ministers "on behalf of the Belgian People". In a joint meeting, both houses of parliament declared the King capable of exercising his powers again the next day.

Question: What is royal assent called in Belgium?


Answer: Council of Ministers

Question: Who declared the monarch incapable of acting upon an abortion decriminalization bill in 1990?


Answer: King Baudouin

Question: Which King refused to sign an abortion decriminalization bill in 1990?


Answer: both houses of parliament

Question: Who declared the King capable of excersizing power again after a brief lapse in 1990?


Answer: six months

Context: The constitution of Jordan grants its monarch the right to withhold assent to laws passed by its parliament. Article 93 of that document gives the Jordanian sovereign six months to sign or veto any legislation sent to him from the National Assembly; if he vetoes it within that timeframe, the assembly may override his veto by a two-thirds vote of both houses; otherwise, the law does not go into effect (but it may be reconsidered in the next session of the assembly). If the monarch fails to act within six months of the bill being presented to him, it becomes law without his signature.

Question: How much time does a Jordinian leader have to sign or veto legislation?


Answer: two-thirds

Question: What majority is required to override a veto from the soverign?


Answer: , it becomes law without his signature

Question: What happens if the soverign doesn't sign the bill within the six-month time frame?


Answer: "The Second Chamber of the States General sends the following approved proposal of law to the First Chamber"

Context: After the House of Representatives has debated the law, it either approves it and sends it to the Senate with the text "The Second Chamber of the States General sends the following approved proposal of law to the First Chamber", or it rejects it and returns it to the government with the text "The Second Chamber of the States General has rejected the accompanying proposal of law." If the upper house then approves the law, it sends it back to the government with the text "To the King, The States General have accepted the proposal of law as it is offered here."

Question: What text is written and sent to the Senate if the House approves of a law?


Answer: The Second Chamber of the States General has rejected the accompanying proposal of law."

Question: What text is written and sent back to the government if a bill is rejected?


Answer: "To the King, The States General have accepted the proposal of law as it is offered here."

Question: If the Senate approves the law after receiving it from the House, what is written and sent to the government?


Answer: the State Magazine

Context: The government, consisting of the monarch and the ministers, will then usually approve the proposal and the sovereign and one of the ministers signs the proposal with the addition of an enacting clause, thereafter notifying the States General that "The King assents to the proposal." It has happened in exceptional circumstances that the government does not approve a law that has been passed in parliament. In such a case, neither the monarch nor a minister will sign the bill, notifying the States General that "The King will keep the proposal under advisement." A law that has received royal assent will be published in the State Magazine, with the original being kept in the archives of the King's Offices.

Question: Where are laws published after receiving assent?


Answer: in the archives of the King's Offices

Question: Where is the original law text stored?


Answer: neither the monarch nor a minister will sign the bill, notifying the States General that "The King will keep the proposal under advisement."

Question: What happens in the rare case the government doesn't approve of a law that has passed both houses?


Answer: Articles 77–79

Context: Articles 77–79 of the Norwegian Constitution specifically grant the monarch of Norway the right to withhold royal assent from any bill passed by the Storting. Should the sovereign ever choose to exercise this privilege, Article 79 provides a means by which his veto may be over-ridden: "If a Bill has been passed unaltered by two sessions of the Storting, constituted after two separate successive elections and separated from each other by at least two intervening sessions of the Storting, without a divergent Bill having been passed by any Storting in the period between the first and last adoption, and it is then submitted to the King with a petition that His Majesty shall not refuse his assent to a Bill which, after the most mature deliberation, the Storting considers to be beneficial, it shall become law even if the Royal Assent is not accorded before the Storting goes into recess."

Question: Which articles in the Norwegian Constitution allow the monarch to reject a bill that has been passed through the Sorting?


Answer: Article 79

Question: Which article in the Norweigan Constitution provides a way to override a monarch's veto?


Answer: two

Question: How many elections are required to assend a bill that the monarch has vetoed?


Answer: Article 92

Context: Title IV of the 1978 Spanish constitution invests the Consentimiento Real (Royal Assent) and promulgation (publication) of laws with the monarch of Spain, while Title III, The Cortes Generales, Chapter 2, Drafting of Bills, outlines the method by which bills are passed. According to Article 91, within fifteen days of passage of a bill by the Cortes Generales, the sovereign shall give his or her assent and publish the new law. Article 92 invests the monarch with the right to call for a referendum, on the advice of the president of the government (commonly referred to in English as the prime minister) and the authorisation of the cortes.

Question: Which article in the Spanish constitution gives the monarch the right to ask for a referendum?


Answer: Article 91

Question: Which article specifies the number of days available to the monarch to provide a signature on an assended bill?


Answer: Title III, The Cortes Generales

Question: In the 1978 Spanish constitution, which title describes how bills are passed?


Answer: Chapter 2, Drafting of Bills

Question: What chapter in the Spanish constitution describes how bills are to be passed?


Answer: "Soy el Rey de España y no el de Bélgica"

Context: No provision within the constitution grants the monarch an ability to veto legislation directly; however, no provision prohibits the sovereign from withholding royal assent, which effectively constitutes a veto. When the Spanish media asked King Juan Carlos if he would endorse the bill legalising same-sex marriages, he answered "Soy el Rey de España y no el de Bélgica" ("I am the King of Spain and not that of Belgium")—a reference to King Baudouin I of Belgium, who had refused to sign the Belgian law legalising abortion. The King gave royal assent to Law 13/2005 on 1 July 2005; the law was gazetted in the Boletín Oficial del Estado on 2 July and came into effect on 3 July 2005. Likewise, in 2010, King Juan Carlos gave royal assent to a law permitting abortion on demand.

Question: What was King Juan Carlos' response to the media when asked if he would sign a bill supporting same-sex marriage?


Answer: a law permitting abortion on demand

Question: What other controversial bill did the king give his assent to in 2010?


Answer: 3 July 2005

Question: When did same-sex marriages become legal in Spain?


Answer: the next person of age in the line of succession

Context: If the Spanish monarch ever refused in conscience to grant royal assent, a procedure similar to the Belgian handling of King Baudouin's objection would not be possible under the current constitution. If the sovereign were ever declared incapable of discharging royal authority, his or her powers would not be transferred to the Cabinet, pending the parliamentary appointment of a regency. Instead, the constitution mandates the next person of age in the line of succession would immediately become regent. Therefore, had Juan Carlos followed the Belgian example in 2005 or 2010, a declaration of incapacity would have transferred power to Felipe, then the heir apparent.

Question: If the Spanish monarch is deemed incapable of granting assent, who is the power transferred to?


Answer: not be possible under the current constitution

Question: Could a Spanish ruler follow the same action of events as King Baudouin did in Belgium?


Answer: 41 and 68

Context: Articles 41 and 68 of the constitution empower the sovereign to withhold royal assent from bills adopted by the Legislative Assembly. In 2010, the kingdom moved towards greater democracy, with King George Tupou V saying that he would be guided by his prime minister in the exercising of his powers. Nonetheless, this does not preclude an independent royal decision to exercise a right of veto. In November 2011, the assembly adopted an Arms and Ammunitions (Amendment) Bill, which reduced the possible criminal sentences for the illicit possession of firearms. The bill was adopted by ten votes to eight. Two members of the assembly had recently been charged with the illicit possession of firearms. The Prime Minister, Lord Tuʻivakanō, voted in favour of the amendment. Members of the opposition denounced the bill and asked the King to veto it, which he did in December.

Question: Which articles allow the soverign to refise consent even when the bills have been passed through the Legislative assembly?


Answer: he would be guided by his prime minister in the exercising of his powers

Question: What statement by King George Tupou emphasized democracy?


Answer: 2011

Question: In which year was the Arms and Ammunitions (Amemndment) Bill adopted?


Answer: December

Question: In what month did the King veto the Arms and Ammunitions Amendment Bill?


Answer: a group

Context: In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely. It allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.

Question: What is an arithmetical structure comprising of a set of elements including an operation that joins any two elements to form a third element?


Answer: group axioms

Question: What is the name used to describe the four conditions of closure, associativity, identity and invertibility?


Answer: abstract formalization of the group axioms

Question: What permits elements with different mathematical starting points to be taken care of in a flexible manner while holding their key basic aspects?


Answer: symmetry

Context: Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity.

Question: What shares an essential relationship to groups?


Answer: Lie groups

Question: What are the symmetry groups utilized as a part of the Standard Model particle physics?


Answer: Point groups

Question: What groups are are utilized toward comprehending symmetry wonders in chemistry?


Answer: Poincaré groups

Question: What groups can express the physical symmetry hidden behind special relativity?


Answer: the study of polynomial equations,

Context: The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right.a[›] To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely (its group representations), both from a theoretical and a computational point of view. A theory has been developed for finite groups, which culminated with the classification of finite simple groups announced in 1983.aa[›] Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.

Question: Where did the idea of a group come from?


Answer: 1870

Question: When was the group notion summed up and solidly settled?


Answer: subgroups, quotient groups and simple groups.

Question: What are smaller and easier to understand groups broken down into?


Answer: 1983

Question: When was announcement for the classification of finite simple groups?


Answer: The set

Context: The set G is called the underlying set of the group (G, •). Often the group's underlying set G is used as a short name for the group (G, •). Along the same lines, shorthand expressions such as "a subset of the group G" or "an element of group G" are used when what is actually meant is "a subset of the underlying set G of the group (G, •)" or "an element of the underlying set G of the group (G, •)". Usually, it is clear from the context whether a symbol like G refers to a group or to an underlying set.

Question: What is known as underlying set of the group?


Answer: the group's underlying set

Question: What is often utilized as a short name for the group?


Answer: shorthand expressions

Question: What expressions are utilized when is really implied to be a longer expression?


Answer: functions

Context: These symmetries are represented by functions. Each of these functions sends a point in the square to the corresponding point under the symmetry. For example, r1 sends a point to its rotation 90° clockwise around the square's center, and fh sends a point to its reflection across the square's vertical middle line. Composing two of these symmetry functions gives another symmetry function. These symmetries determine a group called the dihedral group of degree 4 and denoted D4. The underlying set of the group is the above set of symmetry functions, and the group operation is function composition. Two symmetries are combined by composing them as functions, that is, applying the first one to the square, and the second one to the result of the first application. The result of performing first a and then b is written symbolically from right to left as

Question: What sends a point in the square to the relating point under the symmetry?


Answer: Composing two of these symmetry functions

Question: What gives another symmetry function?


Answer: the dihedral group

Question: What group includes the symmetries of degree 4 and denoted D4?


Answer: Évariste Galois

Context: The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Évariste Galois, extending prior work of Paolo Ruffini and Joseph-Louis Lagrange, gave a criterion for the solvability of a particular polynomial equation in terms of the symmetry group of its roots (solutions). The elements of such a Galois group correspond to certain permutations of the roots. At first, Galois' ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation θn = 1 (1854) gives the first abstract definition of a finite group.

Question: Which French mathematician expanded on earlier work of Paolo Ruffini and Joseph-Louis Lagrange?


Answer: group theory

Question: The journey for answers to polynomial equations of degree higher than 4 was the original motivation for what theory?


Answer: Arthur Cayley

Question: Who developed a theory giving the first abstract definition of a finite group?


Answer: abstract group

Question: What modern concept was created from many fields of mathematics?


Answer: 1870

Context: The convergence of these various sources into a uniform theory of groups started with Camille Jordan's Traité des substitutions et des équations algébriques (1870). Walther von Dyck (1882) introduced the idea of specifying a group by means of generators and relations, and was also the first to give an axiomatic definition of an "abstract group", in the terminology of the time. As of the 20th century, groups gained wide recognition by the pioneering work of Ferdinand Georg Frobenius and William Burnside, who worked on representation theory of finite groups, Richard Brauer's modular representation theory and Issai Schur's papers. The theory of Lie groups, and more generally locally compact groups was studied by Hermann Weyl, Élie Cartan and many others. Its algebraic counterpart, the theory of algebraic groups, was first shaped by Claude Chevalley (from the late 1930s) and later by the work of Armand Borel and Jacques Tits.

Question: When did the uniform theory of groups develop from different sources?


Answer: Walther von Dyck

Question: Who presented a method for specifying a group by means of generators and relations?


Answer: The theory of Lie groups

Question: What theory did Hermann Weyl study in addition to locally compact groups?


Answer: Claude Chevalley

Question: Who initially molded the theory of algebraic groups?


Answer: The University of Chicago

Context: The University of Chicago's 1960–61 Group Theory Year brought together group theorists such as Daniel Gorenstein, John G. Thompson and Walter Feit, laying the foundation of a collaboration that, with input from numerous other mathematicians, classified all finite simple groups in 1982. This project exceeded previous mathematical endeavours by its sheer size, in both length of proof and number of researchers. Research is ongoing to simplify the proof of this classification. These days, group theory is still a highly active mathematical branch, impacting many other fields.a[›]

Question: Where did the group of theorists first meet?


Answer: 1960–61

Question: What university class year belonged to the group of theorists?


Answer: all finite simple groups

Question: What did the group of theorists classify in 1982?


Answer: length of proof and number of researchers.

Question: What two factors describe the large size of the project?


Answer: structural concepts

Context: To understand groups beyond the level of mere symbolic manipulations as above, more structural concepts have to be employed.c[›] There is a conceptual principle underlying all of the following notions: to take advantage of the structure offered by groups (which sets, being "structureless", do not have), constructions related to groups have to be compatible with the group operation. This compatibility manifests itself in the following notions in various ways. For example, groups can be related to each other via functions called group homomorphisms. By the mentioned principle, they are required to respect the group structures in a precise sense. The structure of groups can also be understood by breaking them into pieces called subgroups and quotient groups. The principle of "preserving structures"—a recurring topic in mathematics throughout—is an instance of working in a category, in this case the category of groups.

Question: What ideas are used to understand groups beyond symbols?


Answer: constructions related to groups

Question: What has to be compatible with the group operation?


Answer: group homomorphisms

Question: What concept describes groups that can be related to each other via functions?


Answer: isomorphic

Context: Two groups G and H are called isomorphic if there exist group homomorphisms a: G → H and b: H → G, such that applying the two functions one after another in each of the two possible orders gives the identity functions of G and H. That is, a(b(h)) = h and b(a(g)) = g for any g in G and h in H. From an abstract point of view, isomorphic groups carry the same information. For example, proving that g • g = 1G for some element g of G is equivalent to proving that a(g) ∗ a(g) = 1H, because applying a to the first equality yields the second, and applying b to the second gives back the first.

Question: What are two groups called if they include homomorphisms?


Answer: isomorphic groups

Question: What similar element do isomorphic groups carry?


Answer: applying a to the first equality yields the second

Question: How can showing the second equality yields the first prove the concept of isomorphic groups?


Answer: a rotation

Context: In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]

Question: What is composed of two rotations?


Answer: inverse

Question: What rotation can a rotation be reversed by?


Answer: The subgroup test

Question: What essential condition must be met for a subset of a group to be a subgroup?


Answer: irrelevant to the question whether a reflection has been performed

Context: In many situations it is desirable to consider two group elements the same if they differ by an element of a given subgroup. For example, in D4 above, once a reflection is performed, the square never gets back to the r2 configuration by just applying the rotation operations (and no further reflections), i.e. the rotation operations are irrelevant to the question whether a reflection has been performed. Cosets are used to formalize this insight: a subgroup H defines left and right cosets, which can be thought of as translations of H by arbitrary group elements g. In symbolic terms, the left and right cosets of H containing g are

Question: When is it preferable to consider two group elements to be the same?


Answer: rotation operations

Question: What should not be considered when asking if a reflection has been performed?


Answer: Cosets

Question: What number sets are used to show how subgroups can be seen as translations of the larger group?


Answer: coset addition

Context: This set inherits a group operation (sometimes called coset multiplication, or coset addition) from the original group G: (gN) • (hN) = (gh)N for all g and h in G. This definition is motivated by the idea (itself an instance of general structural considerations outlined above) that the map G → G / N that associates to any element g its coset gN be a group homomorphism, or by general abstract considerations called universal properties. The coset eN = N serves as the identity in this group, and the inverse of gN in the quotient group is (gN)−1 = (g−1)N.e[›]

Question: What is another term for coset multiplication?


Answer: coset multiplication

Question: What group operation is taken by the set from the original group?


Answer: quotient group

Question: What group does the inverse of gN include?


Answer: is the quotient of the free group over the generators of the group

Context: Quotient groups and subgroups together form a way of describing every group by its presentation: any group is the quotient of the free group over the generators of the group, quotiented by the subgroup of relations. The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses. Together with the relations

Question: What groups can be combined to describe every group?


Answer: any group

Question: What group can be the quotient of the free group over the generators of the group?


Answer: every symmetry of the square

Question: What is a finite composition of two symmetries or their inverses?


Answer: injective map

Context: Sub- and quotient groups are related in the following way: a subset H of G can be seen as an injective map H → G, i.e. any element of the target has at most one element that maps to it. The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map G → G / N.y[›] Interpreting subgroup and quotients in light of these homomorphisms emphasizes the structural concept inherent to these definitions alluded to in the introduction. In general, homomorphisms are neither injective nor surjective. Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon.

Question: What map shows the relation between sub and quotient groups?


Answer: surjective maps

Question: What are the opposites of injective maps?


Answer: canonical map

Question: What is an example of a surjective map?


Answer: the first isomorphism theorem

Question: What theory address the phenomenon of homomorphisms being neither injective nor surjective?


Answer: Mathematical objects

Context: Groups are also applied in many other mathematical areas. Mathematical objects are often examined by associating groups to them and studying the properties of the corresponding groups. For example, Henri Poincaré founded what is now called algebraic topology by introducing the fundamental group. By means of this connection, topological properties such as proximity and continuity translate into properties of groups.i[›] For example, elements of the fundamental group are represented by loops. The second image at the right shows some loops in a plane minus a point. The blue loop is considered null-homotopic (and thus irrelevant), because it can be continuously shrunk to a point. The presence of the hole prevents the orange loop from being shrunk to a point. The fundamental group of the plane with a point deleted turns out to be infinite cyclic, generated by the orange loop (or any other loop winding once around the hole). This way, the fundamental group detects the hole.

Question: What are usually analyzed by associating groups to them and studying the elements of the corresponding groups?


Answer: Henri Poincaré

Question: Who founded algebraic topology?


Answer: the fundamental group

Question: What did Henri Poincaré introduce when he established algebraic topology?


Answer: proximity and continuity

Question: What topological properties translate into properties of groups?


Answer: loops

Question: What represents elements of the fundamental group?


Answer: the modulus

Context: In modular arithmetic, two integers are added and then the sum is divided by a positive integer called the modulus. The result of modular addition is the remainder of that division. For any modulus, n, the set of integers from 0 to n − 1 forms a group under modular addition: the inverse of any element a is n − a, and 0 is the identity element. This is familiar from the addition of hours on the face of a clock: if the hour hand is on 9 and is advanced 4 hours, it ends up on 1, as shown at the right. This is expressed by saying that 9 + 4 equals 1 "modulo 12" or, in symbols,

Question: What positive integer is used to divide the sum of two positive integers in modular mathematics?


Answer: the remainder of that division

Question: What results from modular addition?


Answer: a clock

Question: What type of device can be use to demonstrate modular addition?


Answer: modulo p

Context: For any prime number p, there is also the multiplicative group of integers modulo p. Its elements are the integers 1 to p − 1. The group operation is multiplication modulo p. That is, the usual product is divided by p and the remainder of this division is the result of modular multiplication. For example, if p = 5, there are four group elements 1, 2, 3, 4. In this group, 4 · 4 = 1, because the usual product 16 is equivalent to 1, which divided by 5 yields a remainder of 1. for 5 divides 16 − 1 = 15, denoted

Question: What term describes the group of integers related to a prime number?


Answer: 1 to p − 1

Question: What integers are included in modulo p?


Answer: four group elements

Question: How many group elements exist if p=5?


Answer: cyclic

Context: In the groups Z/nZ introduced above, the element 1 is primitive, so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1. Any cyclic group with n elements is isomorphic to this group. A second example for cyclic groups is the group of n-th complex roots of unity, given by complex numbers z satisfying zn = 1. These numbers can be visualized as the vertices on a regular n-gon, as shown in blue at the right for n = 6. The group operation is multiplication of complex numbers. In the picture, multiplying with z corresponds to a counter-clockwise rotation by 60°. Using some field theory, the group Fp× can be shown to be cyclic: for example, if p = 5, 3 is a generator since 31 = 3, 32 = 9 ≡ 4, 33 ≡ 2, and 34 ≡ 1.

Question: What is a group labeled when the element 1 is primitive?


Answer: Any cyclic group with n elements

Question: What group is isomorphic to cyclic groups?


Answer: the group of n-th complex roots of unity

Question: What example of cyclic group satisfies the express of zn = 1?


Answer: Symmetry groups

Context: Symmetry groups are groups consisting of symmetries of given mathematical objects—be they of geometric nature, such as the introductory symmetry group of the square, or of algebraic nature, such as polynomial equations and their solutions. Conceptually, group theory can be thought of as the study of symmetry.t[›] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element performs some operation on X compatibly to the group law. In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too). By a group action, the group pattern is connected to the structure of the object being acted on.

Question: What are groups consisting of symmetries of given arithmetic concepts?


Answer: geometric nature

Question: What term describes the introductory symmetry group of the square?


Answer: group theory

Question: What can regarded as the study of symmetry?


Answer: group law

Question: What is the name of the rule that must be met for a group operation to occur?


Answer: group action

Question: The group pattern is connected to the structure of the target by what behavior?


Answer: group theory

Context: Likewise, group theory helps predict the changes in physical properties that occur when a material undergoes a phase transition, for example, from a cubic to a tetrahedral crystalline form. An example is ferroelectric materials, where the change from a paraelectric to a ferroelectric state occurs at the Curie temperature and is related to a change from the high-symmetry paraelectric state to the lower symmetry ferroelectic state, accompanied by a so-called soft phonon mode, a vibrational lattice mode that goes to zero frequency at the transition.

Question: What aids in predicting changes of physical traits?


Answer: phase transition

Question: What stage of a physical transformation can group theory be used to make prediction?


Answer: Curie temperature

Question: What temperature causes the change of ferroelectric materials?


Answer: soft phonon mode

Question: What term describes the vibrational lattice mode that turns to 0 frequency at the change?


Answer: Mathieu groups

Context: Finite symmetry groups such as the Mathieu groups are used in coding theory, which is in turn applied in error correction of transmitted data, and in CD players. Another application is differential Galois theory, which characterizes functions having antiderivatives of a prescribed form, giving group-theoretic criteria for when solutions of certain differential equations are well-behaved.u[›] Geometric properties that remain stable under group actions are investigated in (geometric) invariant theory.

Question: What are examples of finite symmetry groups used in coding theory?


Answer: coding theory

Question: What is used for error correction of transferred data?


Answer: differential Galois theory

Question: What describes functions having antiderivatives of a prescribed form?


Answer: invariant theory

Question: What concept investigates geometric elements that stay stable under group action?


Answer: Matrix groups

Context: Matrix groups consist of matrices together with matrix multiplication. The general linear group GL(n, R) consists of all invertible n-by-n matrices with real entries. Its subgroups are referred to as matrix groups or linear groups. The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is the special orthogonal group SO(n). It describes all possible rotations in n dimensions. Via Euler angles, rotation matrices are used in computer graphics.

Question: What groups combine matrices with matrix multiplication?


Answer: The general linear group

Question: What includes all invertible n-by-n matrices with real entries?


Answer: matrix groups

Question: What term describes subgroups of the general linear group?


Answer: the special orthogonal group SO(n)

Question: What matrix group portrays all possible rotations in n dimensions?


Answer: Euler angles

Question: Rotation matrix groups are utilized in computer graphics with what concept?


Answer: degree 5 and higher

Context: Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.

Question: What degree does not include simple formulas for cubic and quatric equations?


Answer: Abstract properties of Galois groups

Question: What concept is associated with the solvability of polynomials?


Answer: radicals

Question: What are used to express the solutions of polynomials?


Answer: a finite number of elements

Context: A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups SN, the groups of permutations of N letters. For example, the symmetric group on 3 letters S3 is the group consisting of all possible orderings of the three letters ABC, i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 (or 3 factorial) elements. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group SN for a suitable integer N (Cayley's theorem). Parallel to the group of symmetries of the square above, S3 can also be interpreted as the group of symmetries of an equilateral triangle.

Question: What does a finite group include?


Answer: the order of the group

Question: What is the number of elements in a group named?


Answer: fundamental

Question: What type of class has a finite group that can be expressed as a subgroup of a symmetric group?


Answer: S3

Question: What can be described as the group of symmetries of an equilateral triangle?


Answer: complete classification

Context: Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.

Question: What level of finality do mathematicians try to reach with math concepts?


Answer: finite groups

Question: What area of classification leads to troublesome arithmetic?


Answer: Lagrange's theorem

Question: What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?


Answer: Computer algebra systems

Question: What can be used to classify small groups even though there is no classification of all finite groups?


Answer: The Jordan–Hölder theorem

Question: What describes finite simple groups as the building pieces for all finite groups?