Problem: The Olympic Torch is based on traditional scrolls and uses a traditional Chinese design known as "Lucky Cloud". It is made from aluminum. It is 72 centimetres high and weighs 985 grams. The torch is designed to remain lit in 65 kilometre per hour (37 mile per hour) winds, and in rain of up to 50 millimetres (2 inches) per hour. An ignition key is used to ignite and extinguish the flame. The torch is fueled by cans of propane. Each can will light the torch for 15 minutes. It is designed by a team from Lenovo Group. The Torch is designed in reference to the traditional Chinese concept of the 5 elements that make up the entire universe.
How much does the Olympic Torch weigh?
The answer is the following: 985 grams

Problem: Calculating that no further Russian advance was likely until 1758, Frederick moved the bulk of his eastern forces to Pomerania under the command of Marshal Lehwaldt where they were to repel the Swedish invasion. In short order, the Prussian army drove the Swedes back, occupied most of Swedish Pomerania, and blockaded its capital Stralsund. George II of Great Britain, on the advice of his British ministers, revoked the Convention of Klosterzeven, and Hanover reentered the war. Over the winter the new commander of the Hanoverian forces, Duke Ferdinand of Brunswick, regrouped his army and launched a series of offensives that drove the French back across the River Rhine. The British had suffered further defeats in North America, particularly at Fort William Henry. At home, however, stability had been established. Since 1756, successive governments led by Newcastle and Pitt had fallen. In August 1757, the two men agreed to a political partnership and formed a coalition government that gave new, firmer direction to the war effort. The new strategy emphasised both Newcastle's commitment to British involvement on the Continent, particularly in defence of Germany, and William Pitt's determination to use naval power to seize French colonies around the globe. This "dual strategy" would dominate British policy for the next five years.
Why did Ferdinand feel comfortable withdrawing troops from the eastern front?
The answer is the following: Calculating that no further Russian advance was likely until 1758

Problem: In ultra high vacuum systems, some very "odd" leakage paths and outgassing sources must be considered. The water absorption of aluminium and palladium becomes an unacceptable source of outgassing, and even the adsorptivity of hard metals such as stainless steel or titanium must be considered. Some oils and greases will boil off in extreme vacuums. The permeability of the metallic chamber walls may have to be considered, and the grain direction of the metallic flanges should be parallel to the flange face.
How should the grain direct of metallic flanges run to flange faces?
The answer is the following: parallel

Problem: The Empire was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty. The empire rose to prominence as a culmination of attempts by the southern powers to ward off Islamic invasions by the end of the 13th century. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India. The empire's legacy includes many monuments spread over South India, the best known of which is the group at Hampi. The previous temple building traditions in South India came together in the Vijayanagara Architecture style. The mingling of all faiths and vernaculars inspired architectural innovation of Hindu temple construction, first in the Deccan and later in the Dravidian idioms using the local granite. South Indian mathematics flourished under the protection of the Vijayanagara Empire in Kerala. The south Indian mathematician Madhava of Sangamagrama founded the famous Kerala school of astronomy and mathematics in the 14th century which produced a lot of great south Indian mathematicians like Parameshvara, Nilakantha Somayaji and Jyesthadeva in medieval south India. Efficient administration and vigorous overseas trade brought new technologies such as water management systems for irrigation. The empire's patronage enabled fine arts and literature to reach new heights in Kannada, Telugu, Tamil and Sanskrit, while Carnatic music evolved into its current form. The Vijayanagara Empire created an epoch in South Indian history that transcended regionalism by promoting Hinduism as a unifying factor. The empire reached its peak during the rule of Sri Krishnadevaraya when Vijayanagara armies were consistently victorious. The empire annexed areas formerly under the Sultanates in the northern Deccan and the territories in the eastern Deccan, including Kalinga, while simultaneously maintaining control over all its subordinates in the south. Many important monuments were either completed or commissioned during the time of Krishna Deva Raya. Vijayanagara went into decline after the defeat in the Battle of Talikota (1565).
When was the Kerala school established?
The answer is the following:
14th century