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Who wrote 'The Prince', a work focused on political realism and power?
Niccolò Machiavelli wrote 'The Prince' as a guide for rulers to maintain power.
Areal velocity is defined as the area swept by the position vector per unit time: $\frac{dA}{dt}$.
In polar coordinates, $dA = \frac{1}{2} r^2 d\theta$.
So, $\frac{dA}{dt} = \frac{1}{2} r^2 \frac{d\theta}{dt} = \frac{1}{2} r^2 \omega$.
Since angular momentum $L = m r^2 \omega$, we can substitute $r^2 \omega = \frac{L}{m}$.
Therefore, $\text{Areal Velocity} = \frac{1}{2} \left( \frac{L}{m} \right) = \frac{L}{2m}$.
Given: All omnivores are herbivores. No herbivores are carnivores. Some carnivores are humans. Which conclusions are TRUE? I. Some humans are carnivores. II. No carnivores are omnivores. III. Some omnivores are carnivores.
Conclusion I is true (Some carnivores are humans implies some humans are carnivores). Conclusion II is true (omnivores are herbivores, and no herbivores are carnivores, so no carnivores are omnivores). Conclusion III is false (it contradicts the given statements). So I and II are true.
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