your fearless teacher drops a pendulum at position L, the pendulum swings back toward your teacher's teeth. use the bar graph below to help predict which position (K, L, M) where the pendulum will end up (will it hit the teacher?).

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

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

What component of earth’s atmosphere exists entirely as a result of photosynthesis?