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.

[EX Q]: Vietnamese national hero Le Loi defended his country against this dynasty's forces. The Fish Scale Records were used to calculate taxes by this dynasty's founder, the Hongwu Emperor. This dynasty's Yong-le Emperor ordered the construction of Beijing's Forbidden City. The (*) Yuan Dynasty fell during the Red Turban Rebellion, which brought this dynasty to power. Zheng He was a eunuch admiral who explored under this dynasty's banner. For 10 points, name this Chinese dynasty that began in the 1300s and was renowned for its porcelain.
[EX A]: History

[EX 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.
[EX A]: Science

[EX Q]: It was formed by the union of Chincasuyu, Antisuyu, Kuntisuyu, and Qullasuyu to form the Tahuantinsuyu, or The Four United Provinces, under the rule of Pachacuti. A later leader, Huayna Capac, divided this empire after his death among his two successors, one of whom was captured and executed by Pizarro despite paying a room full of gold as ransom. That last leader was Atahualpa. For 10 points, identify this empire in South America with capital at Cusco.
[EX A]:
History