Three vectors A, B, and C are related to one another such that 5A + 4B = 40C. A fourth vector D exists such that 20C + D = A. Determine an expression for D in terms of the vectors A and B. D =

The “death throes” of stars are amongst the most complex phenomena in all of astronomy, and the “corpses” of stars amongst the most energetic and exotic objects in existence. beginning at the end of the core helium fusion stage in a star’s life, describe in detail the post-main sequence development of both (a) a 1.0 solar mass star, and (b) a 25.0 solar mass star. in what significant ways do they differ? what role does each of these types of stars play in the "star-gas-star" cycle and the evolution of chemical elements in our galaxy?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Imagine that you have two balloons (or, better yet, actually inflate two balloons, if possible). create static electricity around one of the balloons by rubbing it against your hair or your sweater and then bring that balloon close to the other balloon, which has not been charged. try this with at least one other object—and for variety in the discussion, avoid using an object already described by your classmates. then, for your initial post to the discussion, answer the following questions: what happened with the two balloons?