instruction:
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.
question:
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.
answer:
Science


question:
One commander killed in this engagement invented a beech-loading rifle that had earlier been used in the Battle of Brandywine. The Patriot commanders in this battle utilized shifting positions along the base of the central topological entity in this battle, while the leading Loyalist officer's decision to put on a plaid shirt to cover his officer's colors resulted in his demise, as Patriot snipers trained their sights onto the shirt. Colonels John Sevier and William Campbell led part of the Patriot attack at this engagement, and were opposed by Major Patrick Ferguson's force of roughly 1,100 Loyalists. For 10 points, name this Patriot victory in the American Revolution in North Carolina, which followed Horatio Gates' defeat at Camden.
answer:
History


question:
These entities can be hierarchically classified based on the Strahler Order. The speed of objects in this kind of system varies by the sixth power of this system's speed by Brahm's law. Einstein wrote a paper about Baer's law, which claims that the hemisphere of the earth in which these bodies are situated affects erosion. When these bodies form underneath glaciers, they create braided ridges known as eskers. Their cross-sectional area multiplied by their average linear velocity gives their discharge. These bodies create ox-bow lakes when they cut off a meander. For 10 points, name these bodies of water exemplified by the Amazon and Mississippi.
answer:

Social Science