A

Step 1: Define the velocity vectors. The ship's velocity vector is \( \vec{v}_{\text{ship}} = (12, 0) \) m/s (east direction) and the woman's velocity relative to the ship is \( \vec{v}_{\text{woman, ship}} = (0, 5) \) m/s (north direction).
Step 2: To find the woman's velocity relative to the sea, we add the two vectors: \( \vec{v}_{\text{woman, sea}} = \vec{v}_{\text{ship}} + \vec{v}_{\text{woman, ship}} = (12, 0) + (0, 5) = (12, 5) \) m/s.
Step 3: Calculate the magnitude of the woman's velocity relative to the sea using the Pythagorean theorem: \( v = \sqrt{(12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \) m/s.
Step 4: Determine the direction using the tangent function: \( \theta = \tan^{-1}\left(\frac{5}{12}\right) \approx 22.62^\circ \) north of east.
Therefore, the velocity of the woman relative to the sea is 13 m/s at \( 22.62^\circ \) north of east.