When building a home what feature would be the most beneficial in the winter to keeping heat in a home and cold out

Aparticle travels in a circular orbit of radius 21 m. its speed is changing at a rate of 23.1 m/s2 at an instant when its speed is 37.2 m/s. what is the magnitude of the acceleration (in m/s? ) of the particle?

An asteroid is discovered in a nearly circular orbit around the sun, with an orbital radius that is 2.47 times earth's. what is the asteroid's orbital period, its "year," in terms of earth years?

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