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Q2 The last column of the forward kinematic equation of the simple revolute arm is: $$ \begin{bmatrix} P_x \\ P_y \\ P_z \\ 1 \end{bmatrix} = \begin{bmatrix} C_1(L_4C_{234} + L_3C_{23} + L_2C_2) \\ S_1(L_4C_{234} + L_3C_{23} + L_2C_2) \\ L_4S_{234} + L_3S_{23} + L_2S_2 \\ 1 \end{bmatrix} $$ Where $C_i = \operatorname{Cos}\theta_i$; $\theta_i$ is the joint angle of joint $i$; $L_i$ is the length of link $i$. Derive the Jacobian of $P_z$ with respect to the joint variables $\theta_1, \theta_2, \theta_3, \theta_4$.

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Explain why a better understandinf of yourself could be an asset in your internship

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Find equation of line that goes thru point (-3,-2) and perpendicular to line y=(3)/(4)x-2. Write your answer in slope intercept form. Show work

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Presented below are the comparative income and retained earnings statements for Pina Inc. for the years 2025 and 2026. 2026 2025 Sales $316,000 $272,000 Cost of sales 185,000 143,000 Gross profit 131,000 129,000 Expenses 94,600 48,700 Net income $36,400 $80,300 Retained earnings (Jan. 1) $128,600 $75,700 Net income 36,400 80,300 Dividends (31,800) (27,400) Retained earnings (Dec. 31) $133,200 $128,600 The following additional information is provided: 1. In 2026, Pina Inc. decided to switch its depreciation method from sum-of-the-years' digits to the straight-line method. The assets were purchased at the beginning of 2025 for $91,500 with an estimated useful life of 4 years and no salvage value. (The 2026 income statement contains depreciation expense of $27,450 on the assets purchased at the beginning of 2025.) 2. In 2026, the company discovered that the ending inventory for 2025 was overstated by $22,000; ending inventory for 2026 is correctly stated. Prepare the revised retained earnings statement for 2025 and 2026, assuming comparative statements. (Ignore income taxes.) PINA INC. Retained Earnings Statement

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Body dysmorphic disorder used to be characterized as: a somatic physical issue an anxiety disorder a personality disorder a medical issue

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An asset was acquired on August 1, 2024, for $35,000 with an estimated five-year life and $4,400 residual value. The company uses straight-line depreciation. The company calculates partial-year depreciation based on the number of months the asset is in service. What is the gain or loss if the asset was sold for $20,000 on April 30, 2026?

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Write the expression in terms of sine only. 4(sin(2x) - cos(2x))

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Cherry trees in a certain orchard have heights that are normally distributed with =110 inches and standard deviation =14 inches. Find the 25th percentile of the tree heights.

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QUESTION 25 Assume directory1 is a directory. What will be the result of this command? mv newfile directory1/oldfile newfile will be moved to directory1 newfile will be moved to directory1 and will be renamed oldfile The system will give you an error message to the effect that you can't move a file and rename it in the same operation. newfile will be deleted from its current location

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10.9 A silicon npn bipolar transistor is uniformly doped and biased in the forward-active region. The neutral base width is $x_B = 0.8 \mu m$. The transistor doping concentrations are $N_E = 5 \times 10^{17} cm^{-3}$, $N_B = 10^{16} cm^{-3}$, and $N_C = 10^{15} cm^{-3}$. (a) Calculate the values of $p_{E0}$, $n_{B0}$, and $p_{C0}$. (b) For $V_{BE} = 0.625 V$, determine $n_B$ at $x = 0$ and $p_E$ at $x' = 0$. (c) Sketch the minority-carrier concentrations through the device and label each curve.

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shelley c.