Numerade

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Let G = {e, (12)(34), (13)(24), (14)(23)} be the Klein 4-group. Assume that G acts on C[$x_1, x_2, x_3, x_4$] via permutation matrices. Let R = $S^G$ denote the invariant ring. i) Determine whether the image of G in GL(4, C) is generated by pseudo-reflections. ii) Find the Molien series of R. Find a minimal set of generators for R, and find the algebraic relations between them if any. Specify which ones are the primary and secondary invariants

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A 12.5L scuba diving tank contains a helium oxygen mixture of 24.2g of He and 4.32g of O2 at 298K. Calculate the mile fraction

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The 3 times 3 matrix that produces the composite 2D transformation that rotates points through 60 degrees about th using is shown to the right. Show that this transformation is equivalent to a rotation about the origin followed by a translation by p. The 3 imes 3 matrix that produces the composite 2D transformation that rotates points through 60deg about the point (6,9) using homogeneous coordinates is shown to the right. Show that this transformation is equivalent to a rotation about the origin followed by a translation by p. Find p. [[(1)/(2),-(sqrt(3))/(2),3+(9sqrt(3))/(2)],[(sqrt(3))/(2),(1)/(2),(9)/(2)-15sqrt(3)],[0,0,1]] This is equivalent to a rotation through phi =,deg about the origin, followed by a translation by p= (Type an ordered pair. Type an exact answer, using radicals as needed.) Find p. The 3 x 3 matrix that produces the composite 2D transformation that rotates points through 6o about the point (6,9) using homogeneous coordinates is shown to the right. Show that this transformation is equivalent to a rotation about the origin followed by a translation by p. Find p. 1 2 13 9/3 3+ 2 2 V3 2 1 9 -153 2 2 0 0 This is equivalent to a rotation through = about the origin, followed by a translation by p = (Type an ordered pair. Type an exact answer, using radicals as needed.)

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Assume a tissue contains 8 imes 10^5 / cm^2 cells described in problem 1. If the conductance of the interstitial fluid is 2 siemens/ cm^2 (The unit of siemens =1 / Omega ). a. Draw an equivalent circuit. b. If the area of the tissue is 5 cm^2. Calculate the resistance and capacitance for the 5 cm^2 tissue. c. If the stimulus threshold for generating an action potential for individual cell is 20 mV, estimate the current to depolarize all of the cells simultaneously with 60 HzAC source. d. If we use the source with 50 kHz frequency, repeat the estimate for question c. /r/n 1. List five major parts of the conducting system of the heart. What is the function of the SA node and AV node.

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Find all the zeros (real and complex) of P(x) = x4 + 6x3 + 14x2 + 54x + 45. Separate answers with commas. Use exact values, including fractions and radicals, instead of decimals. Enter complex numbers in the form a + bi. Zeros: Write P in factored form as a product of linear and irreducible quadratic factors. Do not use complex linear factors. Be sure to write the full equation, including "P(x) = ". Function:

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Take the real ΔH values for the four compounds from the linked data sources and divide each by the number of moles of O2 that react per mole of fuel. (For example, 3.5 moles of O2 reacts with 1 mole of ethane.) This will give you a ΔH per mole of oxygen for the reaction. What does this result say about the amount of energy that can be released from combustion reactions?

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PROBLEM 3 - The caterpillar The number caterpillar is a rare species of caterpillar, found only in remote jungle areas. Each caterpillar is born with just a head, and a 2 digit number on its face. It grows according to two rules: •If the number is EVEN then the next segment is HALF that number •If the number is ODD then the next segment is ONE MORE than that number. •All caterpillars stop growing when they grow a segment with a 1 on it. Here is a caterpillar starting with the number 13. Find the number on the caterpillars' head that would give the: a. longest b. shortest, caterpillar. My Caterpillar Chart! Name: Date: Goal:

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Sales of products for cash would be included in Net Cash Flow from Operations in the Statement of Cash Flows. True False

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Let U={1, 2, 3, 4, 5, 6, 7}, A={1, 2, 5, 7}, and B={1, 4, 5}. Find $\bar{A} \cap \bar{B}$ \newline $\bar{A} \cap \bar{B}$=\newline (Use a comma to separate answers as needed.)

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For a particular DSB-SC modulator with a carrier frequency of 500 rad/sec, a load resistance of 25 Î©, and a modulating signal given by a(t) = 15 cos(20t), find the following: 1. The peak voltage, Em 2. The carrier frequency, wc 3. The modulation frequency, wm 4. The DSB-SC bandwidth 5. The USB bandwidth and frequencies 6. The LSB bandwidth and frequencies 7. The average power, P 8. The RMS power.

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gonzalo j.