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Quiz 10\quad Apr. 19/21, 1994\cr
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1.   Let $\cal C$ be the unit circle in the $xy$-plane and let $\n$ be the
outward normal vector at each point of $\cal C$. Compute the flux of $\F =
y^2\i - x y\j$ through $\cal C$, $\int_{\cal C} \F\bdot\n \,ds$.
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2. Suppose the temperature at a point $(x,y,z)$ on the unit upper
hemisphere, $x^2+y^2+z^2=1$, $z\ge0$, is given by $T(x,y,z) =
(x^2+y^2)z$. Compute the average temperature over the hemisphere.
(The area of the hemisphere is $2\pi$.)

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