2013 nfl football draft

- 2013 2013 12013 6 6 .
Quora Her (2013 movie): In the movie "Her", where do the OS's go?
GB/T 29601-2013 GB4806.9-2016 .
20122013 .
15 (12) RM.
IMDB7.0/10 7.7/10 74%69% (?).
PA13 2199 .
2013320
20133mmThe Key .
20131625

Quora Her (2013 movie): In the movie "Her", where do the OS's go?
GB/T 29601-2013 GB4806.9-2016 .
20122013 .
15 (12) RM.
IMDB7.0/10 7.7/10 74%69% (?).
PA13 2199 .
2013320
20133mmThe Key .
20131625
Solution: For vectors to be orthogonal, their dot product must be zero: $\mathbf{m} \cdot \mathbf{n} = x(1) + 2(-1) = x - 2 = 0$. Solving gives $x = 2$. The final answer is $\boxed{2}$.
Question: A science policy analyst evaluates the spread of a technology using roots of $z^4 + z^2 + 1 = 0$. The maximum imaginary part of a root can be expressed as $\sin\theta$. Find $\theta$ in radians.
Solution: Let $w = z^2$, so $w^2 + w + 1 = 0$. Solving gives $w = \frac{-1 \pm \sqrt{-3}}{2} = e^{\pm 2\pi i/3}$. Thus, $z^2 = e^{\pm 2\pi i/3}$, so $z = e^{\pm \pi i/3 + \pi i k/2}$ for $k = 0, 1$. The roots have angles $\pi/3, 5\pi/3, 7\pi/3, 11\pi/3$, but
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