Input: Group (mathematics)
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.

What describes functions having antiderivatives of a prescribed form?
Output: differential Galois theory

Input: Seven Years%27 War
The War of the Austrian Succession had seen the belligerents aligned on a time-honoured basis. France's traditional enemies, Great Britain and Austria, had coalesced just as they had done against Louis XIV. Prussia, the leading anti-Austrian state in Germany, had been supported by France. Neither group, however, found much reason to be satisfied with its partnership: British subsidies to Austria had produced nothing of much help to the British, while the British military effort had not saved Silesia for Austria. Prussia, having secured Silesia, had come to terms with Austria in disregard of French interests. Even so, France had concluded a defensive alliance with Prussia in 1747, and the maintenance of the Anglo-Austrian alignment after 1748 was deemed essential by the Duke of Newcastle, British secretary of state in the ministry of his brother Henry Pelham. The collapse of that system and the aligning of France with Austria and of Great Britain with Prussia constituted what is known as the "diplomatic revolution" or the "reversal of alliances."

What was the major gain by Great Britain by having Austria as it ally?
Output: British subsidies to Austria had produced nothing of much help to the British

Input: Incandescent light bulb
During ordinary operation, the tungsten of the filament evaporates; hotter, more-efficient filaments evaporate faster. Because of this, the lifetime of a filament lamp is a trade-off between efficiency and longevity. The trade-off is typically set to provide a lifetime of several hundred to 2,000 hours for lamps used for general illumination. Theatrical, photographic, and projection lamps may have a useful life of only a few hours, trading life expectancy for high output in a compact form. Long-life general service lamps have lower efficiency but are used where the cost of changing the lamp is high compared to the value of energy used.

What determines how fast a tungsten filament evaporates?
Output: hotter, more-efficient filaments evaporate faster

Input: Age of Enlightenment
French historians traditionally place the Enlightenment between 1715, the year that Louis XIV died, and 1789, the beginning of the French Revolution. Some recent historians begin the period in the 1620s, with the start of the scientific revolution. The Philosophes, the French term for the philosophers of the period, widely circulated their ideas through meetings at scientific academies, Masonic lodges, literary salons and coffee houses, and through printed books and pamphlets. The ideas of the Enlightenment undermined the authority of the monarchy and the church, and paved the way for the revolutions of the 18th and 19th centuries. A variety of 19th-century movements, including liberalism and neo-classicism, trace their intellectual heritage back to the Enlightenment.

In what decade did the scientific revolution begin?
Output:
1620s