Figure 22-32 shows three rods, each with the same charge Q spread uniformly along its length. Rods a (of length L) and b (of length L/2) are straight, and points P are aligned with their midpoints. Rod c (of length L/2) forms a complete circle about point P. Rank the rods according to the magnitude of the electric field they create at points P, greatest first.

In the image, the arrow is pointing to a celestial object. which attribute disqualifies the object from being a planet?

A33.1 g copper object is launched from a 1.5 m 30° steel incline positioned on the floor by being pulled up a string attached to a 50.0 g mass suspended vertically over a pulley. the object is projected towards a glass table where it lands when it is at the point along its trajectory with the lowest speed. it comes to a halt when it clears the opposite edge of the table. it then falls and lands on 9 physics texts each 5 cm thick that are stacked on the floor on the opposite side of the table. assume that the table does not have a ledge and the rectangular object experiences 0.05 n of air resistance as it falls towards the books. how far and how long did the object travel and how fast does it hit the books. assume that at the moment the copper object leaves the incline, the massless string and ideal pulley break off

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning