The stabilizing control problem of a Remotely Operated Vehicle (ROV) for a submarine observing operation is solved explicitly using a homogeneous time-varying controller. We prove that the ROV kino-dynamic model fails the Brockett's necessary condition, consequently, the system's equilibrium cannot be stabilized using continuous pure state feedback laws. Our control strategy is based on a continuous time-varying feedback law taking into account coupling terms due to underactuation and nonlinearities. It is shown that the feedback law stabilizes the ROV at the origin, and this is illustrated by simulations.