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📰 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 📰 How Many Days Until Daylight Saving Time 5540730 📰 How To Say Thank You In Korean Words 7854646 📰 Microsoft Project Viewer The Sophisticated Tool Free For Instant Project Management 212801 📰 Vidmate Latest Version 2983739 📰 Typical Retirement Age 8088539 📰 The Shocking Truth Flat Piercing Youve Never Seen Before Has Stunned Salon Owners 7624379 📰 Wukong Game Is Taking Over Heres Why You Need To Download It Now 6530675 📰 Lxeh Stock Shock Is This The Next Market Disruptor You Cant Ignore 387267 📰 Kennedy Jr 6605977 📰 The Grooms Best Friend Did Something Shockingthe Groomsmans Hidden Hero Moment 9742295 📰 The Shocking Secrets Revealed About Chrome Rivers Hidden Waters You Wont Believe What Lies Beneath 1189124 📰 Crests Silksong 5797039 📰 Breakung News 2928920 📰 Side Effects Of Lexapro In Women 7694473 📰 Best Savings Rate Interest 2796236