In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

[Q]: This philosopher argued that the only way to exercise freedom is to act morally, because otherwise one's actions are bound by one's conditional desires. This thinker defined the title concept of one of his essays as "man's emergence from his self-imposed immaturity." He postulated that our senses perceive only phenomena and not noumena, so we can never truly know the "thing-in-itself." This author of "What is Enlightenment" argued that we should act only according to maxims that could be made universal law, which he called the "categorical imperative." For 10 points, name this German author of Groundwork of the Metaphysics of Morals and Critique of Pure Reason.
[A]: Social Science


[Q]: Laplaces rule may be used to compute a version of this quantity for its namesake tensor in order to prove the Alon-Tarsi conjecture for Latin squares of even order; that proof uses Cayleys version of this operator. The Cauchy-Binet rule generalizes it to commutative rings, while Leibnizs formula uses permutations of elements to compute it. Setting to zero the result of this operation on lambda I minus A allows us to calculate As eigenvalues. Cramers rule uses ratios of these to solve systems of linear equations. For ten points, name this quantity that is a d minus c b for a 2 by 2 matrix a b c d.
[A]: Science


[Q]: Following his resignation due to a failed harvest, the pipiolos and Diego Portales jockeyed for power. Jose Miguel Carrera shifted allegiances to and from this man, and led the aristocratic opposition to his rule. The illegitimate son of the viceroy of Peru, he led the army that was defeated at Rancagua. Later, he was one of two men who led the victory at Chacabuco, along with Jose de San Martin. For 10 points, name this South American revolutionary, who from 1817 to 1823 was the ruler of Chile.
[A]:
History