B

When the cork is removed from the opening at A, the pressure inside the vessel will change due to the centrifugal force acting on the water as the vessel rotates.
Step 1: Understand that when a liquid is in a rotating reference frame, it experiences a centrifugal force that effectively pushes it outward.
Step 2: Upon removing the cork, the centrifugal force will cause the water to push out of the opening.
Step 3: Since point A is at the axis of rotation, the water will flow in the direction opposite to the centrifugal force, leading to a jet of water exiting the container.
Conclusion: Therefore, the water will flow out of the opening at A as long as the vessel is rotating, confirming that the correct answer is option B.