Input: Read this: Symmetry groups are groups consisting of symmetries of given mathematical objectsbe 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 term describes the introductory symmetry group of the square?

Output: geometric nature

QUES: At the end of the 16th century, England and the Netherlands began to challenge Portugal's monopoly of trade with Asia, forming private joint-stock companies to finance the voyagesthe English, later British, East India Company and the Dutch East India Company, chartered in 1600 and 1602 respectively. The primary aim of these companies was to tap into the lucrative spice trade, an effort focused mainly on two regions; the East Indies archipelago, and an important hub in the trade network, India. There, they competed for trade supremacy with Portugal and with each other. Although England ultimately eclipsed the Netherlands as a colonial power, in the short term the Netherlands' more advanced financial system and the three Anglo-Dutch Wars of the 17th century left it with a stronger position in Asia. Hostilities ceased after the Glorious Revolution of 1688 when the Dutch William of Orange ascended the English throne, bringing peace between the Netherlands and England. A deal between the two nations left the spice trade of the East Indies archipelago to the Netherlands and the textiles industry of India to England, but textiles soon overtook spices in terms of profitability, and by 1720, in terms of sales, the British company had overtaken the Dutch.

When was the Dutch East India Company chartered?
What is the answer?
ANS: 1602

QUES: While pursuing his PhD at Princeton, Feynman married his high school sweetheart, Arline Greenbaum (often misspelled "Arlene"), despite the knowledge that she was seriously ill with tuberculosisan incurable disease at the time. She died in 1945. In 1946, Feynman wrote a letter to her, expressing his deep love and heartbreak, that he kept for the rest of his life. ("Please excuse my not mailing this," the letter concluded, "but I don't know your new address.") This portion of Feynman's life was portrayed in the 1996 film Infinity, which featured Feynman's daughter, Michelle, in a cameo role.
Which disease did Arline overcome?

ANS: unanswerable

The French planned to invade the British Isles during 1759 by accumulating troops near the mouth of the Loire and concentrating their Brest and Toulon fleets. However, two sea defeats prevented this. In August, the Mediterranean fleet under Jean-Francois de La Clue-Sabran was scattered by a larger British fleet under Edward Boscawen at the Battle of Lagos. In the Battle of Quiberon Bay on 20 November, the British admiral Edward Hawke with 23 ships of the line caught the French Brest fleet with 21 ships of the line under Marshal de Conflans and sank, captured, or forced many of them aground, putting an end to the French plans.
If it is possible to answer this question, answer it for me (else, reply "unanswerable"): Where was the planned invasion of Britain by France?
Ah, so.. near the mouth of the Loire

Question: The Cardinal Camerlengo of the Holy Roman Church, assisted by the Vice-Camerlengo and the other prelates of the office known as the Apostolic Camera, has functions that in essence are limited to a period of sede vacante of the papacy. He is to collate information about the financial situation of all administrations dependent on the Holy See and present the results to the College of Cardinals, as they gather for the papal conclave.
Try to answer this question if possible: Who has functions that are not limited to a period of sede vacante of the papacy?
Answer: unanswerable

Problem: The creation of a modern industrial economy took place. With the creation of a transportation and communication infrastructure, the corporation became the dominant form of business organization and a managerial revolution transformed business operations. In 1890, Congress passed the Sherman Antitrust Actthe source of all American anti-monopoly laws. The law forbade every contract, scheme, deal, or conspiracy to restrain trade, though the phrase "restraint of trade" remained subjective. By the beginning of the 20th century, per capita income and industrial production in the United States exceeded that of any other country except Britain. Long hours and hazardous working conditions led many workers to attempt to form labor unions despite strong opposition from industrialists and the courts. But the courts did protect the marketplace, declaring the Standard Oil group to be an "unreasonable" monopoly under the Sherman Antitrust Act in 1911. It ordered Standard to break up into 34 independent companies with different boards of directors.
What creations brought in the modern industrial economy?
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Answer:
transportation and communication infrastructure