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Find the rotation matrix of a point " P " if its frame ( B ) is rotated 30^(-)about Y-axis relative to frame (A). ( 15 Mark) Frame ( B ) is rotated relative to frame ( A ) about Y-axis by 60\deg . Find hat(A)R, then find ^(A)P if ^(A)P={30-5}^(TT). (15 Mark) Vector ^(A)P_(1) is rotated relative to frame ( A ) about x-axis by 30\deg , and translated 5,7 and 3 units in x_(c),Y_(A) and Z respectively. Define the transformation matrix (T) then find ^(A)P_(2) if ^(A)P_(1)=[[1,3,4]]^(7), (15 Mark) Write the transformation equation for ^(B)^(B) T, and _(A)^(C)T. (15 Mark) 5- Describe frame {B} relative to frame {A} if the origin of (B) is positioned at 1,2 and 3 in x,Y and Z relative to frame ( A ) and ( B ) is rotated 45\deg about the X -axis relative to frame ( A ). ( 15 Mark ) 6- Frame ( B ) is rotated relative to frame ( A ) about Z-axis by 30\deg and translated 4 units in x-axis and 3 units in Y-axis. Find the transformation matrix that describes frame ( A ) relative to frame ( B ). ( 25 Mark)

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Assuming the octet rule is obeyed, how many covalent bonds will an oxygen atom form to give a formal charge of zero? Group of answer choices 4 1 0 2 3

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mary recieved an inheritance of $50,000. she invested part at 15% and deposited the remainder in tax free bonds at 5%. her total annual income from the investments was $5200. find the amount invested

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What are the shortcomings of CRISPR-Cas9? How might new versions of CRISPR address some of these limitations?

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According to the Katha Upanishad - What is the central debate that emerges between Nachiketas and Death (Yama)? Death wants Nachiketas to have one set of values, while Nachiketas argues something else should be more important; what are these contrasting values? What do you think is the text's message, and what do you take away from this document that has influenced so many of today's religions?

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Part 1 A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 348,000 gallons. Tank cars with three different carrying capacities are available: 6,000 gallons, 12,000 gallons, and 24,000 gallons. Letting t=number of 24,000 railroad tank cars in the fleet, 2t−8 6,000-gallon railroad tank cars, and −3t+33 12,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 6,000-gallon tank car is $550 per month, a 12,000-gallon tank car is $850 per month, and a 24,000-gallon tank car is $1050 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost? Question content area bottom Part 1 enter your response here 6,000-gallon tank cars, enter your response here 12,000-gallon tank cars, and enter your response here 24,000-gallon tank cars.

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Q2. Do $18 \cdot 37^{211}$ and $17 + 12^{99}$ have the same remainder when divided by 24? Justify your answer.

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If we have a data frame loaded in R's global environment and we want to save it as a table in PostgreSQL, what do we need to do first? • Export the data frame as a .tar file Export the data frame as a .csv file We can't transfer the file Establish a connection from R to PostgreSQL

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Question 3 Solve the following equation, giving your answer in exact form. $x^4 - 4x^2 + 21 = 0$ (5 marks)

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During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 636 & 645 & 712 & 707 & 835 & 820 & 810 & 870 & 856 & 923 & 878 & 937 & 948 \\ \hline y & 100 & 92 & 89 & 85 & 76 & 75 & 74 & 63 & 57 & 55 & 47 & 43 & 38 \\ \hline \end{tabular} $\sum x_i = 10,577$, $\sum y_i = 894$, $\sum x_i^2 = 8,742,161$, $\sum y_i^2 = 66,232$, $\sum x_i y_i = 703,251$ (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) (b) Compute the estimated standard deviation $s_{\beta_1}$. (Round your answer to four decimal places.) (c) Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. (Round your answers to three decimal places.) Does it appear that this true average change has been precisely estimated? $\circ$ This is a fairly wide interval, so $\beta_1$ has been precisely estimated. $\circ$ This is a fairly narrow interval, so $\beta_1$ has not been precisely estimated. $\circ$ This is a fairly narrow interval, so $\beta_1$ has been precisely estimated. $\circ$ This is a fairly wide interval, so $\beta_1$ has been precisely estimated. $\circ$ This is a fairly wide interval, so $\beta_1$ has not been precisely estimated.

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sandra m.