Answer
$$\left( {3\sqrt 2 , - \frac{\pi }{4},7} \right)$$
Work Step by Step
$$\eqalign{
& \left( {3, - 3,7} \right) \cr
& \left( {x,y,z} \right):{\text{ }}\left( {3, - 3,7} \right) \to x = 3,{\text{ }}y = - 3,{\text{ }}z = 7 \cr
& {\text{Rectangular to cylindrical}} \cr
& {r^2} = {x^2} + {y^2} \to r = \sqrt {{{\left( 3 \right)}^2} + {{\left( { - 3} \right)}^2}} = 3\sqrt 2 \cr
& \tan \theta = \frac{y}{x} \to \theta = {\tan ^{ - 1}}\left( {\frac{{ - 3}}{3}} \right) = - \frac{\pi }{4} \cr
& z = z \to z = 7 \cr
& {\text{The cylindrical coordinates are:}} \cr
& \left( {3\sqrt 2 , - \frac{\pi }{4},7} \right) \cr} $$
