A fluid moves so that its velocity is \vec {u} \equiv (2xt,-yt,-zt) , written in rectangular Cartesian coordinates. Show that the surface F(x,y,z,t) = x^2exp (-2t^2)+(y^2+2z^2)exp(t^2)=constant moves with the fluid (so that it always contains the same fluid particles; that is, DF/Dt=0)...