11. Let $x: E^2 \to T$ be the parametrization of the torus given in Example 2.6.
In each case below, show that the formula
$F(x(u, v)) = x(f(u, v), g(u, v))$
is consistent (Exercise 10), and describe the resulting mapping
$F: T \to T$. (For example, give its effect on the meridians and parallels
of $T$.)
(a) $f = 3u, g = v$.
(b) $f = u + \pi, g = v + 2\pi$.
(c) $f = v, g = u$.
(d) $f = u + v, g = u - v$.
Which of these mappings are diffeomorphisms?
