Problem 1: Expanded Knowledge
Python Code 2: Eulerian velocity evaluation at selected spatial points
selected_points = [(0.5, 0.5), (2.0, 8.0), (-0.8, 0.3)]
for (xp, yp) in selected_points:
    vx = A * yp
    vy = -S * xp
    speed = np.sqrt(vx**2 + vy**2)
    print(
        f"Point (x, y) = ({xp:.2f}, {yp:.2f}) : "
        f"v = ({vx:>7.2f}, {vy:>7.2f}) , "
        f"|v| = {speed:>7.2f}"
    )
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