It is in the news that all these pitiful kin
Are to be bought out and mercifully gathered in
To live in villages, next to the theatre and the store.
Where they won't have to think for themselves anymore,
While greedy good-doers, beneficent beasts of prey,
Swarm over their lives enforcing benefits
That are calculated to soothe them out of their wits,
And by teaching them how to sleep they sleep all day
Destroy their sleeping at night the ancient way. (A Roadside Stand)
Let \( \vec{p} \) and \( \vec{q} \) be two unit vectors and \( \alpha \) be the angle between them. Then \( (\vec{p} + \vec{q}) \) will be a unit vector for what value of \( \alpha \)?
A cylindrical tank of radius 10 cm is being filled with sugar at the rate of 100π cm3/s. The rate at which the height of the sugar inside the tank is increasing is: