Context and question: Matrix groups consist of matrices together with matrix multiplication. The general linear group GL(n, R) consists of all invertible n-by-n matrices with real entries. Its subgroups are referred to as matrix groups or linear groups. The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is the special orthogonal group SO(n). It describes all possible rotations in n dimensions. Via Euler angles, rotation matrices are used in computer graphics.
What are subgroups of the special orthogonal group called?
Answer: unanswerable
Context and question: The origins of the Ashkenazim are obscure, and many theories have arisen speculating about their ultimate provenance. The most well supported theory is the one that details a Jewish migration through what is now Italy and other parts of southern Europe. The historical record attests to Jewish communities in southern Europe since pre-Christian times. Many Jews were denied full Roman citizenship until 212 CE, when Emperor Caracalla granted all free peoples this privilege. Jews were required to pay a poll tax until the reign of Emperor Julian in 363. In the late Roman Empire, Jews were free to form networks of cultural and religious ties and enter into various local occupations. But, after Christianity became the official religion of Rome and Constantinople in 380, Jews were increasingly marginalized.
Many Jews were denied full Roman citizenship until what year?
Answer: 212 CE
Context and question: The Farmington Canal Trail is a rail trail that will eventually run continuously from downtown New Haven to Northampton, Massachusetts. The scenic trail follows the path of the historic New Haven and Northampton Company and the Farmington Canal. Currently, there is a continuous 14-mile (23 km) stretch of the trail from downtown, through Hamden and into Cheshire, making bicycle commuting between New Haven and those suburbs possible. The trail is part of the East Coast Greenway, a proposed 3,000-mile (4,800 km) bike path that would link every major city on the East Coast from Florida to Maine.
What rail trail is slated to run between downtown New Haven and Northampton, Massachusetts?
Answer:
The Farmington Canal Trail