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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

Question 7 [2 marks] in the circuit below, the electromotive force generated by the battery is e = 6.0 v, and the resistances are r1 = r4 = 1.0 q, r2 = r3 =2.0 q. r. the power delivered by the battery to the circuit is closest to a. 6 w в. 12 w с. 15 w d. 18 w e. 20 w final exam autumn 2014 page 5 of 9 68037 physical modelling faculty of science [2 mark] question 8 with reference to question 7, the current through resistor r2 is closest to a. 1 a в. 2 а c. 3 a d. 4 a e. 6 a

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.