The coordinates of the point in the ${x}^{\text{'}}{y}^{\text{'}}$ - coordinate system with the given angle of rotation and the xy-coordinates.

waigaK
2020-11-17
Answered

The coordinates of the point in the ${x}^{\text{'}}{y}^{\text{'}}$ - coordinate system with the given angle of rotation and the xy-coordinates.

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lamanocornudaW

Answered 2020-11-18
Author has **85** answers

Suppose the x- and y- axes are rotated about the origin through a positive acute angle

Given:

The angle of rotation is

Calculation:

Use the definition, substitute the values of x-, y- coordinates and

Know that

Thus, the

=1

Therefore, the coordinates of the point the

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A majorette in a parade is performing some acrobatic twirlingsof her baton. Assume that the baton is a uniform rod of mass 0.120 kg and length 80.0 cm.

With a skillful move, the majorette changes the rotation ofher baton so that now it is spinning about an axis passing throughits end at the same angular velocity 3.00 rad/s as before. What is the new angularmomentum of the rod?

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A vertex of a minimum vertex cut has a neighbor in every component

I'm trying to understand the solution for the following problem: Prove that ${\kappa}^{\prime}(G)=\kappa (G)$ when G is a simple graph with $\mathrm{\Delta}(G)\le 3$.

The solution goes like this: Let S be the minimum vertex cut, $|S|=\kappa (G)$. Since $\kappa (G)\le {\kappa}^{\prime}(G)$ always, we need only provide an edge cut of size |S|. Let ${H}_{1}$ and ${H}_{2}$ be two components of G-S. Since S is a minimum vertex cut, each $v\in S$ has a neighbor in ${H}_{1}$ and a neighbor in ${H}_{2}$. The solution conntinues from here...I really have no clue why the part "Since S is a minimum vertex cut, each $v\in S$ has a neighbor in ${H}_{1}$ and a neighbor in ${H}_{2}$." is true.

I tried to show it by contradiction but haven't gotten very far: Suppose otherwise; then there exists a vertex $v\in S$ which doesn't have a neighbor in ${H}_{1}$. We can assume that G is connected, hence there is a path joining v with $u\in V({H}_{1})$... and I'm stuck. How do I proceed from here? Or should I try to prove this in a completely different way?

I'm trying to understand the solution for the following problem: Prove that ${\kappa}^{\prime}(G)=\kappa (G)$ when G is a simple graph with $\mathrm{\Delta}(G)\le 3$.

The solution goes like this: Let S be the minimum vertex cut, $|S|=\kappa (G)$. Since $\kappa (G)\le {\kappa}^{\prime}(G)$ always, we need only provide an edge cut of size |S|. Let ${H}_{1}$ and ${H}_{2}$ be two components of G-S. Since S is a minimum vertex cut, each $v\in S$ has a neighbor in ${H}_{1}$ and a neighbor in ${H}_{2}$. The solution conntinues from here...I really have no clue why the part "Since S is a minimum vertex cut, each $v\in S$ has a neighbor in ${H}_{1}$ and a neighbor in ${H}_{2}$." is true.

I tried to show it by contradiction but haven't gotten very far: Suppose otherwise; then there exists a vertex $v\in S$ which doesn't have a neighbor in ${H}_{1}$. We can assume that G is connected, hence there is a path joining v with $u\in V({H}_{1})$... and I'm stuck. How do I proceed from here? Or should I try to prove this in a completely different way?

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The matrix:

$Q=\left[\begin{array}{cc}-1& 2\\ 0& 1\end{array}\right]$

The matrix:

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a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued)

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Response rates to Web surveys are typically low, partially due to users starting but not finishing the survey. The factors that influence response rates were investigated in Survey Methodology (Dec. 2013). In a designed study, Web users were directed to participate in one of several surveys with different formats. For example, one format utilized a welcome screen witb a white background, and another format utilized a welcome screen with a red background. The "break-off rates," i.e., the proportion of sampled users who break off the survey before completing all questions, for the two formats are provided in the table.

a) Verify the values of the break-off rates shown in the table.

b) The researchers theorize that the true break-off rate for Web users of the red welcome screen will be lower than the corresponding break-off Tate for users of the white welcome screen. Give the null and alternative hypotbesis for testing this theory.

c) Conduct the test, part b, at