A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v=w(-yi+xj). a. Sketch, on a separate sheet of paper, the vector field with w=1 and the vector field with w=-1. Then determine the speed Vert{vâ}Vert of the vortex as a function of the distance from its center, r.
b. Compute div vâ and curl vâ.
c. Compute the circulation of vâ counterclockwise about the circle of radius R in the xy-plane, centered at the origin.

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.

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