91Ó°ÊÓ

Estimate the product of 4,308,229 and 44 to one significant figure (show your work and do not use a calculator), and express the result in standard scientific notation.

Find the vector \(\vec{C}\) that satisfies the equation \(3 \hat{x}+6 \hat{y}\) \(10 \hat{z}+\vec{C}=-7 \hat{x}+14 \hat{y}\)

Sketch the vectors with the components \(\vec{A}=\left(A_{x}, A_{y}\right)=\) \((30.0 \mathrm{~m},-50.0 \mathrm{~m})\) and \(\vec{B}=\left(B_{x}, B_{y}\right)=(-30.0 \mathrm{~m}, 50.0 \mathrm{~m}),\) and find the magnitudes of these vectors.

What angle does \(\vec{A}=\left(A_{x}, A_{y}\right)=(30.0 \mathrm{~m},-50.0 \mathrm{~m})\) make with the positive \(x\) -axis? What angle does it make with the negative \(y\) -axis?

Sketch the vectors with the components \(\vec{A}=\left(A_{x}, A_{y}\right)=\) \((-30.0 \mathrm{~m},-50.0 \mathrm{~m})\) and \(\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m}),\) and find the magnitudes of these vectors.

What angle does \(\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m})\) make with the positive \(x\) -axis? What angle does it make with the positive \(y\) -axis?

A position vector has components \(x=34.6 \mathrm{~m}\) and \(y=-53.5 \mathrm{~m} .\) Find the vector's length and angle with the \(x\) -axis.

For the planet Mars, calculate the distance around the Equator, the surface area, and the volume. The radius of Mars is \(3.39 \cdot 10^{6} \mathrm{~m}\)

Find the magnitude and direction of each of the following vectors, which are given in terms of their \(x\) - and \(y\) -components: \(\vec{A}=(23.0,59.0),\) and \(\vec{B}=(90.0,-150.0)\)

Find the magnitude and direction of \(-\vec{A}+\vec{B},\) where \(\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)\)