Which of the following commands would you use to sharply adjust the ship's course to the right?

The command to use for sharply adjusting the ship's course to the right is "hard right rudder." This command instructs the helmsman to turn the ship's rudder fully to the right, enabling a quick and sharp change in direction. This maneuver allows for immediate course adjustments which are essential in scenarios requiring rapid responses, such as avoiding obstacles or navigating tight spaces.

Other options may imply different actions that are not suited for a sharp right turn. For instance, "full astern" indicates a command to reverse the ship's engines, which does not change the ship's direction to the right but rather moves it backwards. "Starboard pivot" suggests a turning motion but does not necessarily indicate the specific action of using the rudder to achieve a quick turn. "Right full" may refer to an action intended to turn the ship to the right, but it lacks the clarity of specifying that the rudder should be turned sharply. Thus, "hard right rudder" is the most precise and effective command for making a drastic right turn.