C

The $1000\mathrm{kg}$ heavy satellite is transported to the orbit $150\mathrm{km}$ above the ground. Find the mechanical work required for this transport. The mass of the Earth is $M=6\cdot {10}^{24}\mathrm{kg}$, gravitational constant $\kappa =6.67\cdot {10}^{-11}{\mathrm{N}\mathrm{m}}^2{\mathrm{kg}}^{-2}$ and Earth radius $R=6370\mathrm{km}$. Round your result to nearest $\mathrm{MJ}$.

A homogeneous cube with the side $10\mathrm{cm}$ is in the water. The bottom side is parallel to the water surface $10\mathrm{cm}$ below the surface. Find the work required to move the cube to the position when the bottom side just touches the surface of the water. The mass density of the cube is $2000{\mathrm{kg}\mathrm{m}}^{-3}$, the mass density of the water is $1000{\mathrm{kg}\mathrm{m}}^{-3}$ and the standard acceleration of gravity is $g=10{\mathrm{m}\mathrm{s}}^{-2}$.

Evaluate the following integral on $\mathbb{R}$. $$\int {\cos }^{3}x\sin x\mathrm{d}x$$

The force of the repulsion of two charged particles is $$F(x)=\frac{c}{x^2},$$ where $x$ is the distance in meters and $c$ a positive constant. Find the work required to increase the distance between the particles from $3\mathrm{m}$ to $1\mathrm{m}$.