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: In this work, a definition of justice as "what is good for the stronger" is given by Thrasymachus. In this work, a story about the killer of King Candaules of Lydia is used to describe how people are just out of necessity. That story in this work tells of the [*] "Ring of Gyges." This work describes chained prisoners who watch shadows pass before them. This work combines ideas about the "divided line" and the sun into its "Allegory of the Cave." For 10 points, name this work that proposes a government ruled by philosopher kings, a dialogue on government by Plato.

SOLUTION: Literature

PROBLEM: One protagonist in this novel spends a summer with the wife of Colonel Forster, and that character's aunt and uncle have the surname Gardiner. One character in this novel initially rejects a marriage proposal by Mr. Collins, while her sister is romanced by Mr. Bingley, and another romance in this novel is initiated by the master of Pemberley, Mr. Darcy. For 10 points, name this novel about the sisters of the Bennet family, one of whom is Elizabeth, by Jane Austen.

SOLUTION: Literature

PROBLEM: A spherical harmonic can be decomposed into N times an exponential times the associated Legendre polynomial of THIS function. The wavelength shift in Compton scattering is equal to the Compton wavelength times one minus this function. The square of this function appears multiplied by the incident intensity to give the emitted intensity of a polarizer in (*) Malus' Law. This function appears on the top left and the bottom right entry on the standard 2 by 2 rotation matrix. For a block on an incline, this function multiplied by the force of gravity gives the magnitude of the normal force. For two vectors, the dot product is equal to their magnitude multiplied by this function of the angle between them. For 10 points, name this function which is also used to find the x-component of a given vector.

SOLUTION:
Science