answer:Central Bank C should increase the quantity of money, but to a lesser extent than if it only cared about stabilizing one of those variables. This will help to offset the decrease in velocity and partially stabilize both the price level and output.

answer:The angle theta between two vectors can be found using the dot product formula: cos(theta) = frac{mathbf{A} cdot mathbf{B}}{|mathbf{A}| |mathbf{B}|} Calculating the dot product and the magnitudes: begin{align*} mathbf{A} cdot mathbf{B} &= left(-frac{17}{2}right)left(-frac{15}{2}right) + left(-frac{13}{2}right)left(frac{19}{2}right) + 5left(frac{5}{2}right) + left(frac{11}{2}right)left(-frac{1}{2}right) &= frac{255}{4} - frac{247}{4} + frac{25}{2} - frac{11}{4} &= frac{47}{4} end{align*} Magnitude of mathbf{A}: |mathbf{A}| = sqrt{left(-frac{17}{2}right)^2 + left(-frac{13}{2}right)^2 + 5^2 + left(frac{11}{2}right)^2} = sqrt{frac{289}{4} + frac{169}{4} + 25 + frac{121}{4}} = sqrt{11543} Magnitude of mathbf{B}: |mathbf{B}| = sqrt{left(-frac{15}{2}right)^2 + left(frac{19}{2}right)^2 + left(frac{5}{2}right)^2 + left(-frac{1}{2}right)^2} = sqrt{frac{225}{4} + frac{361}{4} + frac{25}{4} + frac{1}{4}} = sqrt{1554} Now, find the angle theta: cos(theta) = frac{frac{47}{4}}{sqrt{11543} cdot sqrt{1554}} theta = cos^{-1}left(frac{47}{4 cdot sqrt{11543 cdot 1554}}right) theta = cos^{-1}left(frac{47}{6 sqrt{11543}}right) Therefore, the angle between the two vectors is cos^{-1}left(frac{47}{6 sqrt{11543}}right).

answer:A binary star is a star system consisting of two stars that orbit around a common center of mass. Alpha Centauri is a binary star system located in the southern constellation of Centaurus. It is the closest star system to the Sun, at a distance of about 4.37 light-years. The two stars in the Alpha Centauri system are Alpha Centauri A and Alpha Centauri B. Alpha Centauri A is a Sun-like star, while Alpha Centauri B is a red dwarf star. Alpha Centauri

answer:To add these two matrices, we add corresponding elements: left( begin{array}{c} frac{25}{6} + left(-frac{13}{2}right) -frac{59}{6} + frac{1}{6} end{array} right) Now, convert the mixed fractions to improper fractions for easier addition: left( begin{array}{c} frac{25}{6} + frac{39}{6} -frac{59}{6} + frac{1}{6} end{array} right) Add the elements: left( begin{array}{c} frac{64}{6} -frac{58}{6} end{array} right) Simplify by dividing both terms by their greatest common divisor, which is 2: left( begin{array}{c} frac{32}{3} -frac{29}{3} end{array} right) However, there seems to be a mistake in the provided answer. The correct answer is: left( begin{array}{c} frac{32}{3} -frac{29}{3} end{array} right)