Problem: Group (mathematics):

In the groups Z/nZ introduced above, the element 1 is primitive, so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1. Any cyclic group with n elements is isomorphic to this group. A second example for cyclic groups is the group of n-th complex roots of unity, given by complex numbers z satisfying zn = 1. These numbers can be visualized as the vertices on a regular n-gon, as shown in blue at the right for n = 6. The group operation is multiplication of complex numbers. In the picture, multiplying with z corresponds to a counter-clockwise rotation by 60. Using some field theory, the group Fp can be shown to be cyclic: for example, if p = 5, 3 is a generator since 31 = 3, 32 = 9 4, 33 2, and 34 1.

What are numbers on an irregular n-gon?
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A: unanswerable

Problem: Steven Spielberg:

The Science Fiction Hall of Fame inducted Spielberg in 2005, the first year it considered non-literary contributors. In November 2007, he was chosen for a Lifetime Achievement Award to be presented at the sixth annual Visual Effects Society Awards in February 2009. He was set to be honored with the Cecil B. DeMille Award at the January 2008 Golden Globes; however, the new, watered-down format of the ceremony resulting from conflicts in the 200708 writers strike, the HFPA postponed his honor to the 2009 ceremony. In 2008, Spielberg was awarded the Legion d'honneur.

In what year was the Science Fiction Hall of Fame created?
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A: unanswerable

Problem: Philosophy of space and time:

But in statistical mechanics things get more complicated. On one hand, statistical mechanics is far superior to classical thermodynamics, in that thermodynamic behavior, such as glass breaking, can be explained by the fundamental laws of physics paired with a statistical postulate. But statistical mechanics, unlike classical thermodynamics, is time-reversal symmetric. The second law of thermodynamics, as it arises in statistical mechanics, merely states that it is overwhelmingly likely that net entropy will increase, but it is not an absolute law.

What is an abso;ute law in statistical mechanics?
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A: unanswerable

Problem: Gene:

The relationship between genes can be measured by comparing the sequence alignment of their DNA.:7.6 The degree of sequence similarity between homologous genes is called conserved sequence. Most changes to a gene's sequence do not affect its function and so genes accumulate mutations over time by neutral molecular evolution. Additionally, any selection on a gene will cause its sequence to diverge at a different rate. Genes under stabilizing selection are constrained and so change more slowly whereas genes under directional selection change sequence more rapidly. The sequence differences between genes can be used for phylogenetic analyses to study how those genes have evolved and how the organisms they come from are related.

What does comparing the sequence alignment of genes' DNA measure?
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A:
The relationship between genes