A Thin Spherical Shell

2. A thin spherical shell of radius x₁ cm has x₂ µC of charge uniformly distributed over its surface. What is the electric flux through an area of x₃ m² of a spherical surface concentric with the shell of charge but having a radius of x₄ m?

x₁, x₂, x₃, and x₄ are some numbers.
Answer: 8.99∙10⁴∙ x₂ ∙ x₃ / x₄² N∙m²/C

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General Physics

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Escape Velocity

What is the escape velocity of a rocket launched from position A, the center of the three planet system depicted in the figure. Each planet has mass M, radius R, and the distance between the center of any planet and position A is r. 

A Ball is Thrown

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What is Magnitude of Angle between Vectors?

The vector A = (A_x , A_y) = ( +2.0 m, +2.0 m) and the vector B = (B_x , B_y) = ( +1.0 m, -1.0 m).
What is the magnitude of the angle between the vectors A and B? 

Intermediate calculations (by Google Search):
arccos(((2.05 * 1.05) - (1.95 * 0.95)) / (sqrt(2.05 * 1.95) * sqrt(0.95 * 1.05))) = 81.3594657 degrees
arccos(((1.95 * 0.95) - (2.05 * 1.05)) / (sqrt(2.05 * 1.95) * sqrt(0.95 * 1.05))) = 98.6405343 degrees

Solution: 90 ± 9 degrees

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