A

The escape velocity is given by the formula:
$$ v_e = \sqrt{\frac{2GM}{R}} $$
where:
- $v_e$ is the escape velocity,
- $G$ is the universal gravitational constant,
- $M$ is the mass of the planet (in this case, Earth),
- $R$ is the radius of the planet.
Notice that the escape velocity $v_e$ does not include the mass of the projectile (rocket) itself. Therefore, the escape velocity of a rocket launched from the surface of the earth does not depend on the mass of the rocket. Hence, the correct answer is option A.