Let ø = p(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is the position vector. Show that %3D div (Tu) = u · div T + tr (T grad u)

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What is the curl of a vector field? How can you interpret it?

A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)