21. Which of the following is NOT considered a good leaving group? в се AOH CHOH 22 are less stable, thus more reactive in a polar aprotic solvent. Polar aprotic Potential energy Protic Reaction coordinate A. Anions/Nucleophiles B. Cations/Electrophiles/Alkyl halides
30 3 0 - і в холиод туйлвэд ләвол ла! Бачтеrу оf t° Р“м (т
A. I В. М С. II Ф. E. None 4. Select the expected product from the reaction shown. CI- OD ? OD II IV
(2) (a) For any O E [ 0 21] let -sino Cose x For Cosce sino 1² [ a b ] simplity any matrix A АХ 052 If A = and [33]... B =[2] C], find X-sored that A(x+B) = C. Q 2 (C) Let S be the set of matrices of the form As a a2 ag where arbitrary real numbers. Show there exists a unique matrix E in s such that A EA for all o in وگرنه...
5-4. Prove that the MGF of Gamma distribution is В f(t) В — t. 5-5. Let X1, X2,... ,X be independent with X~ Gamma (ai,ß). Let Y = EX4. Prove that Y Gamma (Eai,ß)
complete measure space (i.e. ВЕА, "(В) — 0, АсВ — АЄ (5) Let (Q, A, м) be a A, u(A) = 0). Let f,g : Q+ R* be a pair functions. Assume that f is measurable g almost everywhere and that f (a) Prove that g is measurable (b) Let A E A and assume that f is integrable on A. Prove that g is integrable on A and g du complete measure space (i.e. ВЕА, "(В) — 0, АсВ...
4. Consider the configuration below which carry the current Jo for t < 0 I(t) = 1 for t20 That is, a constant current I, is turned on abruptly at t=0. Find the resulting retarded vector potential at point P. (Hint: Be careful and indicate when point P sees" various parts of the wire.)
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
eoge D М 21) Suppose the demand for money in the small country is = 0.5Y. Assume P P 1, then Y- real minay Supply a) b) $900 $1500 $2000 $2400
(a) 1.9 M CH3COONa/1.0 M CH,COOH (b) 0.2 М СН,СОONa/0.1 M CH,CОон. Which is the more effective buffer? 1.9 М СH,COONa/1.0 M СH,сОон А. 0.2 M CH3COON a/0.1 M CH3COOH В.