A peacock mantis shrimp smashes its prey with a hammer-like appendage by storing energy in a springlike section of exoskeleton on its appendage. The spring has a force constant of $5.9 \times 10^4 \mathrm{~N} / \mathrm{m}$. What power does the shrimp generate if it unleashes the energy in $0.0018$ s? (The power per mass of the shrimp appendage is more than 20 times greater than that generated by muscle alone, showcasing the shrimp's ability to harness the potential energy of its spring.)

The integral represents the volume of a solid. Sketch the region and axis of revolution that produce the solid. $\int_{0}^{1} 2 \pi x\left(x-x^{2}\right) d x$

Define Poisson's ratio.

Explaining the clues you use, make inferences about the speaker's character in (a) lines $31$-$43$ of "My Last Duchess" and (b) lines $18$- $20$ of "Life in a Love."

A torque of $650\ \mathrm{Nm}$ rotates a shaft of diameter $0.25 \mathrm{~m}$ with $\omega=50\ \mathrm{rad} / \mathrm{s}$. What are the shaft surface speed and the transmitted power?

The elongation E of a spring balance varies directly with the applied weight W. If E = 3 when W = 20, find E when W = 15.

The lines $y=2 x+3$ and $y=a x+5$ are parallel if a = _____.

You have a fixed length $L$ of wire and wish to make a single loop that will experience the maximum torque in a magnetic field. Is it better to make the coil circular or square, or doesn't it matter?

Vocabulary: Sex ratio

Find the moment of inertia about the z-axis of the solid cone $\sqrt{x^2 + y^2} \leqslant z \leqslant h$. Assume that the solid has constant density $k$.

The power output (in watts) of a certain brand of wind turbine generators is estimated to be

$$P=f(R, V)=0.772 R^2 V^3$$

where $R$ is the radius (in meters) of a rotor blade and $V$ is the wind speed (in meters per second). Estimate the power output of a model of these generators if its radius is $30 \mathrm{~m}$ and the wind speed is $16 \mathrm{~m} / \mathrm{s}$.

The space between two 6 -in.-long concentric cylinders is filled with glycerin (viscosity $\mu = 8.5 \times 10^{-3} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2} )$. The inner fills the 0.001- in. gap between the rotating shaft and the stationary base. Determine the frictional torque on the shaft when it rotates at 5000 $\mathrm{rpm}$.

Mendel studied a tall variety of pea plants with stems that are 20 cm long and a dwarf variety with stems that are only 12 cm long. A. Under blending theory, how long would you expect the stems of first and second hybrids to be? B. Under Mendelian rules and assuming stem length is controlled by a single gene, what would you expect to observe in the second-generation hybrids if all the first-generation hybrids were tall?

Described the relationship of the two graphed lines.