Asteroids can be classified into two broad groups based on their composition and location: carbon-rich asteroids dominate the outer part of the asteroid belt, whereas metal-rich asteroids dominate the inner part of the belt. analysis of the fragment we have discussed in this project reveals that it contains nearly equal amounts of metals and carbon. can you conclude that the original whole asteroid had a similar composition? can you conclude with a high degree of confidence that the asteroid originated in the middle regions of the asteroid belt? explain your reasoning. if you would need more data from the asteroid analysis, what would you like to see?

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

19. explain why a magnet from your refrigerator could not be used to lift something as heavy as a car. (chapter 7 – pages 202-203) 20. can a magnet ever have a single pole? explain your answer. (chapter 7 – page 208) 21. what happens to the wavelength of a wave if the frequency is increased? (chapter 9 – pages 280-281) 22. an ocean wave has a wavelength of 10 m and a frequency of 4.0 hz. what is the velocity of the wave? show the appropriate equation from your book and show your work with units. (chapter 9 – page 282) 23. as you sit outside, the sound of a siren becomes lower in pitch. is the emergency vehicle moving away from or towards you? explain how you know. (chapter 10 – page 315-316) 24. why are two astronauts in space unable to hear one another? (chapter 10 – page 307) 25. explain in at least 3 sentences how electromagnetic waves form. (chapter 11 – page 338-339) 26. using the chart on page 345 in your textbook, what are the three types of electromagnetic wave with wavelengths shorter than those of visible light. give an example of each. (chapter 11 – pages 345-351) 27. explain why a leaf usually appears to be green, but a rose typically appears red. (chapter 12 – page 373) 28. what is the difference in light that is refracted compared to light that is reflected? think in terms of speed of light as well as what happens to light waves when they interact with a medium. (chapter 12 – pages 369-370) 29. how are concave and convex lenses different? (chapter 13 – page 408-410) 30. what type of mirror is used in rearview mirrors in cars? why is it important that these mirrors have the warning, “objects in mirror are closer than they appear.”? (chapter 13 – page 405)

Alinearly polarized electromagnetic wave has an average intensity of 196 w/m^2. this wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). polarizer a is oriented with its transmission axis at an angle of θ_1=20.8∘ with the incident electric field. polarizer b has its axis at an angle of θ_2=63.0∘ with the incident electric field. what is the average intensity of the wave after it passes through polarizer a? what is the average intensity of the wave after it passes through polarizer b? suppose that the two polarizers a and b are interchanged. what would the average intensity be after passing through both polarizers?