Your tank vessel is fully loaded, and you find that she is down slightly by the head. To adjust the trim, which action may you take?

To adjust the trim of a tank vessel that is slightly down by the head, shifting cargo aft is the most effective means among the provided methods. When you shift cargo aft, you effectively move the center of gravity toward the stern, which raises the bow and improves the trim of the vessel. This method can be done quickly and without the need for additional materials, thus allowing for immediate adjustments to the vessel's balance.

Adding ballast aft or loading more cargo aft could also potentially help with the trim. However, these options involve either bringing additional weight into the vessel or changing the existing ballast, which could take more time and may not be readily feasible depending on the cargo and ballast management protocols in place. Shifting cargo is a standard practice and aligns well with efficiency and safety considerations on tankers.

In summary, shifting cargo aft directly impacts the vessel's center of gravity and trim in a way that is both immediate and controllable, making it the most suitable choice for adjusting the vessel's trim for better performance and stability.