# Scientific Research Projects

Question

Do cell phones cause cancer? This is a multibillion dollar question. There are currently dozens of lawsuits pending that claim cell phones use caused cancer. To help shed light on the issue, several scientific research projects have been undertaken. One such project was conducted by Danish researchers. This 13-year study examined 420,000 Danish cell phone users. The scientists determined the number of Danes who would be expected to contract various forms of cancer. The expected number and the actual number of cell phone users who developed each type of cancer are listed below. Cancer Expected Number Actual Number Brain and nervous system 143 135 Salivary glands 9 7 Leukemia 80 77 Pharynx 52 32 Esophagus 57 42 Eye 12 8 Thyroid 13 13

a) Can we infer from these data that there is a relationship between cell phone use and cancer?

b) Discuss the results, including whether the data are observational or experimental. provide several interpretations of the statistics. in particular, indicate whether you can infer that cell phone use causes cancer.

Question

f and g are both affine transformations, the transformation f is reflection in the line y=2, and the transformation g maps the points (0,0), (1,0) and (0,1) to the points (1,1), (2,2) and (3,-1) respectively
(a) Determine g (in the form g(x)=Ax+a, where A is a 2×2 matrix, and a is a vector with two components
(b) Express f as a composite of three transformations: a translation, followed by a reflection in a line through the origin, followed by a translation. Hence determine f (in the same form as found g in part (a))
(c) Use the expression found for f(x) and g(x) in parts (a) and (b) to calculate f(g(x)), and hence find the affine transformation f o g, in the same for as you found g in part (a)
(d) Use your  answer to part (c) to determine any points (x,y) that are left unchanged by the transformation f o g, or show that there are no such points (find any values of x and y for which f(g(x,y)) = (x,y))

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