If you double the temperature of a blackbody, by what factor will the total energy radiated per second per square meter increase ?

Solve Construction Problem 9.3.4.

Draw the condensed and line-angle structural formula for the following compound: butyraldehyde

Solve each compound inequality. Graph the solution. 6x ≤ -18 or 2x > 18

For the following problem,

a. Plot the graph using a window set to show the entire graph, when possible. Sketch the result.

b. Give the y-intercept and any x-intercepts and the locations of any vertical asymptotes.

c. Give the range.

Rational function $y=\frac{x^2-2 x-2}{x-3}$ with the domain $-2 \leq x \leq 6, x \neq 3$

Creating uses. List five garments in your wardrobe. Describe two new ways to wear each one.

Draw the condensed and line-angle structural formula for the following compound: acetone

Se encontró el cadáver de una mujer en el bosque. Algunas fibras de pelo encontradas en el cuerpo fueron enviadas al laboratorio criminalístico para su análisis. Las puntas del pelo pegado al cuerpo eran grises, pero las puntas del pelo mostraban que había sido teñido. La distancia desde la raíz del pelo hasta el comienzo de la zona teñida medía $8\text{ mm}$. Los investigadores determinaron que el cabello de la víctima se había teñido por última vez el $1$ de agosto de $2004$. Suponiendo que el cabello crece a razón de $0.44\text{ mm}$ al día, ¿en qué fecha murió la mujer aproximadamente? Explique su respuesta.

Multiplying a vector by a matrix is a much more complicated process than multiplying a vector by a scalar. However, in certain special cases, matrix and scalar multiplication can lead to the same result. If $\mathbf{A} \vec{v}=\lambda \vec{v}$ where $\mathbf{A}$ is a matrix, $\vec{v}$ a nonzero vector, and $\lambda$ a scalar, then $\vec{v}$ is said to be an eigenvector of $\mathbf{A}$, and $\lambda$ is said to be an eigenvalue of $\mathbf{A}$. For instance, let

$$\mathbf{A}=\left(\begin{array}{cc}-2 & -1 \\ 8 & 7\end{array}\right), \overrightarrow{v_1}=(1,-8)$$

, and $\lambda_1=6$. We have:

$$\begin{array}{ll} \mathbf{A} \vec{v}_1=\left(\begin{array}{cc} -2 & -1 \\ 8 & 7 \end{array}\right) \cdot\left(\begin{array}{c} 1 \\ -8 \end{array}\right)=\left(\begin{array}{c} 6 \\ 1 \\ -48 \end{array}\right)=\left(\begin{array}{c} 6 \\ -48 \end{array}\right) . \\ \lambda_1 \vec{v}_1= & 6 \cdot\left(\begin{array}{c} 6 \\ -8 \end{array}\right) \end{array}$$

We see that multiplying $\vec{v}_1$ by $\lambda_1=6$ works out the same as multiplying $\vec{v}_1$ by $\mathbf{A}$; we say that $\vec{v}_1$ is an eigenvector of $\mathbf{A}$ with an eigenvalue of $\lambda_1=6$.

(a) Show that $\vec{v}_2=(1,-1)$ is an eigenvector of $\mathbf{A}$. What is the eigenvalue?

(b) Show that $\vec{v}_3=(-3,3)$ is an eigenvector of $\mathbf{A}$. What is the eigenvalue?

(c) If $\vec{v}$ is an eigenvector of $\mathbf{A}$, explain why the vectors $\vec{v}$ and $\mathbf{A} \vec{v}$ are parallel.

In the mentioned exercise, if the coin is assumed fair, then, for n=2, what are the probabilities associated with the values that $X$ can take on?

Teachers who expect more from students often get more. This is an example of a(n) ____________ prophecy.

Show that no such matrices A and B exist such that AB-BA=I

Base your answers to question on the following diagram of Earth. Some of the latitude and longitude lines have been labeled. Points $A$ through $\mathrm{E}$ represent locations on Earth's surface.

The latitude and longitude of which location are closest to those of New York State?

(1) $\mathrm{A}$

(2) B

(3) C

(4) D

Evaluate the indefinite integral.

$$\int 5 e^{0.3 x} d x$$