During the Vector Addition lab, Mac and Tosh start at the classroom door and walk 40.0 m, north, 32.5 m east, 15.5 m south, 68.5 m west, and 2.5 m, north. Determine the magnitude and direction of the resultant
displacement of Mac and Tosh.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

4. now look at the green lines you created by connecting the three boiling point data points and the three melting point data points. for each of these lines, describe any trends you see. 5. locate the elements on your periodic table that you circled in green on your graph. what term or description would you use to identify these elements with respect to the periodic table? 7. using the room temperature line (orange line) and your periodic table, make lists that identify the state of matter (gas, liquid, or solid) in which each element you plotted exists at room temperature. explain your answers.

If a rock is thrown upward on the planet mars with a velocity of 10 mys, its height in meters t seconds later is given by y − 10t 2 1.86t 2 . (a) find the average velocity over the given time intervals: (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] (v) [1, 1.001] (b) estimate the instantaneous velocity when t − 1.