Please all the three questions

4. If S is a smooth surface, define the notion of a smooth function S -> R. Show that, if S is a smooth surface, each component of the inclusion map S - R3 is a smooth function S -> R. 5. Show that translations and invertible linear transformations of R3 take smooth surfaces to smooth surfaces. 6. Let y be a regular curve in the xy-plane given by (t) = (u(t), v(t), 0 ). Let S be the subset of R3 obtained by revolving y about the x-axis. If 0 denotes the angle of rotation from the xy-plane, verify that o (t, 0) = (u(t), v(t) cos 0, v(t) sin 0) defines a patch on S. Is this a regular patch