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: A failed naval expedition led by this country's Blanco Encalada resulted in the 1837 Treaty of Paucarpata, while its 1925 Constitution began its Presidential Republic period. This modern day country was captured in a campaign led by Pedro de Valdivia; that campaign saw fighting against its native Araucanian or Mapuche Indians. This country's Patria Vieja period of independence was ended at the Disaster of Rancagua. Its independence campaign was led by men like the Carrera Brothers and Bernardo O'Higgins, and the 19th century saw the flourishing of its free port Valparaiso. For 10 points, name this South American country led in the 20th century by Salvador Allende and Augusto Pinochet.

SOLUTION: History

PROBLEM: One antagonist in this work leaves behind the head of Aeschere after killing him. Unferth argues that the success of this work's title character was due to luck. A villager steals a golden cup from a cave towards the end of this work. The title character  beheads the corpse of a figure who had been attacking Herot and decides to help King Hrothgar at its beginning. At the end of this work, Wiglaf helps the protagonist battle a dragon which ultimately kills the hero. For 10 points, name this epic poem about a hero who killed the monster Grendel.

SOLUTION: Literature

PROBLEM: The values of this property along certain lines are the semi-major axes of the Poinsot ellipse; the colatitude partial derivative of this quantity is zero along those lines, which are known as geometric principle axes. For planar translations, this property transforms by Steiner's theorem, which can be derived directly when one considers this quantity as a contravariant rank-two symmetric tensor. Its magnitude is equal to an object's area of gyration times its mass. For 10 points, identify the material property that is equal to the integral over a body of distance from an axis with respect to mass, is symbolized I, and is the rotational analogue of mass.

SOLUTION:
Science