TASK DEFINITION: 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.
PROBLEM: The final ruler of this dynasty severed his daughter's arm in an attempt to kill his entire family during its final days. In one criminal case, this dynasty saw an expansion of the "Nine Exterminations" to also include the killing of friends as well as family members. The Cathedral of the Immaculate Conception was founded in this dynasty's capital by one of its advisors, Matteo Ricci. This dynasty dispatched the treasure ships of the admiral Zheng He and moved the empire's capital from Nanking. It was founded by a former leader of the Red Turban rebellion, the Hongwu Emperor. For 10 points, name this Chinese dynasty that made Beijing the capital, succeeded the Mongols, and was itself supplanted by the Manchus in the 1640's.

SOLUTION: History

PROBLEM: Lindstrom's theorem states that first-order logic is the strongest logic having both this property and satisfying the Lowenheim-Skolem property. A method for finding a Hausdorff space with this property containing a given space is named for Stone and Cech. Equicontinuity is the main condition for determining whether a family of functions has this property by the Arzela-Ascoli theorem. Using the axiom of choice, it can be shown that an arbitrary product of spaces with this property has this property, a result known as Tychonoff's theorem. In Euclidean space, being closed and bounded is sufficient to show, according to the Heine-Borel theorem, that a set has this property. For 10 points, identify this property which holds of a set on which every open cover has a finite subcover.

SOLUTION: Science

PROBLEM: It is based on "Nach Unterdruckung der Burschenschaft", "Der Landesvater", "Fuchs Lied", and "Gaudeamus Igitur. " Composed during a vacation at Ischl in 1880, the composer of this work became acquainted with the songs on which it is based when he spent a month with his friend Joseph Joachim at the University of Gttingen. FTP, name this work written for the occasion of the University of Breslau awarding an honorary doctorate to the composer, Johannes Brahms.

SOLUTION:
Fine Arts