Answer:
θ = Cos⁻¹[A.B/|A||B|]
A. The angle between two nonzero vectors can be found by first dividing the dot product of the two vectors by the product of the two vectors' magnitudes. Then taking the inverse cosine of the result
Explanation:
We can use the formula of the dot product, in order to find the angle between two non-zero vectors. The formula of dot product between two non-zero vectors is written a follows:
A.B = |A||B| Cosθ
where,
A = 1st Non-Zero Vector
B = 2nd Non-Zero Vector
|A| = Magnitude of Vector A
|B| = Magnitude of Vector B
θ = Angle between vector A and B
Therefore,
Cos θ = A.B/|A||B|
<u>θ = Cos⁻¹[A.B/|A||B|]</u>
Hence, the correct answer will be:
<u>A. The angle between two nonzero vectors can be found by first dividing the dot product of the two vectors by the product of the two vectors' magnitudes. Then taking the inverse cosine of the result</u>
<u>The motions of the gas and stars at the center indicate that it contains 4 million solar masses within a region no larger than our solar system</u> is the evidence supports the existence of a very massive black hole at the center of our galaxy.
<h3>
What is black hole?</h3>
Black holes are points in space that are so dense they create deep gravity sinks. Beyond a certain region, not even light can escape the powerful tug of a black hole's gravity. And anything that ventures too close—be it star, planet, or spacecraft—will be stretched and compressed like putty in a theoretical process aptly known as spaghettification.
There are four types of black holes: stellar, intermediate, supermassive, and miniature. The most commonly known way a black hole forms is by stellar death. As stars reach the ends of their lives, most will inflate, lose mass, and then cool to form white dwarfs. But the largest of these fiery bodies, those at least 10 to 20 times as massive as our own sun, are destined to become either super-dense neutron stars or so-called stellar-mass black holes.
Learn more about black holes
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Answer:
Option A
Explanation:
This can be explained based on the conservation of energy.
The total mechanical energy of the system remain constant in the absence of any external force. Also, the total mechanical energy of the system is the sum of the potential energy and the kinetic energy associated with the system.
In case of two stones thrown from a cliff one vertically downwards the other vertically upwards, the overall gravitational potential energy remain same for the two stones as the displacement of the stones is same.
Therefore the kinetic energy and hence the speed of the two stones should also be same in order for the mechanical energy to remain conserved.
Answer:
The energy dissipated as the puck slides over the rough patch is 1.355 J
Explanation:
Given;
mass of the hockey puck, m = 0.159 kg
initial speed of the puck, u = 4.75 m/s
final speed of the puck, v = 2.35 m/s
The energy dissipated as the puck slides over the rough patch is given by;
ΔE = ¹/₂m(v² - u²)
ΔE = ¹/₂ x 0.159 (2.35² - 4.75²)
ΔE = -1.355 J
the lost energy is 1.355 J
Therefore, the energy dissipated as the puck slides over the rough patch is 1.355 J
