Consider two vectors in two dimension, a whose magnitude is a and direction is with the angel a with respect to the +x direction, and b whose magnitudes b and direction is with the angle beta with the x axis. show that the addition vector from a + b have the maximum magnitude when these two vectors point in the same direction, i. e., alpha = beta.

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

Connie has $660,000 she wants to save. if the fdic insurance limit per depositor, per bank, is $250,000, which of these way is distributing her money between three banks will guarantee that all of her money is insured ?

Aboat radioed a distress call to a coast guard station. at the time of the call, a vector a from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. a vector from the station to the point where the boat was later found is = 30.0 km, 15.0° north of east. what are the components of the vector from the point where the distress call was made to point where the boat was found? in other words, what are the components of vector c = b - a?