Final answer:
The angular velocity of a wheel rotating counterclockwise in the xy-plane points out of the page, and if the rotation rate is slowing down, the angular acceleration is negative and directed into the page.
Step-by-step explanation:
When discussing a wheel rotating counterclockwise in the xy-plane, we typically use the right-hand rule to determine the direction of its angular velocity. If the wheel's angular velocity is decreasing, this implies that the angular acceleration is in the opposite direction to the angular velocity. With the wheel rotating counterclockwise, the angular velocity vector points out of the page (towards you).
Thus, if the rotation rate is slowing down, the angular acceleration is directed into the page. According to physics convention, counterclockwise rotation is assigned a positive direction. Hence, a decreasing counterclockwise rotation rate indicates that the angular acceleration is negative when the angular velocity decreases.