I.10.14 Flux of the vector field

Condition: For a vector field \( \vec{F}(x, y, z)=\left(x z, y z, z^{2}\right) \) find the flow through the surface \( S \), where \( S \) is the part \( z=2 \) cut out by the surface \( \left\{\begin{array}{c}x^{2}+y^{2}+z^{2}=9 \\ z \text { decreases }\end{array}\right. \).