Use the Divergence Theorem to calculate the flux of the vector fields $\vec F_1 = -7z\vec i + 7x\vec k$ and $\vec F_2 = -7z\vec i + (y+2)\vec j + 7x\vec k$ through the surface $S$ given by the sphere of radius $a$ centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically.

With $W$ giving the interior of the sphere,
$\int_S\vec F_1\cdot d\vec A = \int_W$ $dV =$
and
$\int_S\vec F_2\cdot d\vec A = \int_W$ $dV =$