Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Answer:
D. A record of all the physical activity you complete in one week.
Explanation:
A "Fitness Log" allows you to keep track of your workout or exercise. Therefore, it is <em><u>a record of the different workout you've managed to complete within a time frame</u></em>. It gives you several information such as the<em> type of workout you've completed, its duration and the time of the day it was performed</em>. This makes a person motivated to exercise because he can see his progress. He may also include <em>his mood before and after workout</em> in order to become more mindful in exercising and many other things.
Answer:
22510.8J
Explanation:
Given parameters:
Mass of lead = 4.68kg
Initial temperature = 25°C
Final temperature = 62°C
Unknown:
The heat needed to cause this temperature change = ?
Solution:
To solve this problem, we use the expression below:
H = m c Ф
H is the quantity of heat
m is the mass
c is the specific heat capacity
Ф is the temperature change
So;
Specific heat capacity of lead = 130J/kg°C
Insert the parameters and solve;
H = 4.68 x 130 x (62 - 25) = 22510.8J
Answer:
the radius of the protons path is r = 0.85 m.
Explanation:
the force due to magnetic fields lead to the cetripetal force, such that:
F = q×v×B = m×(v^2)/r
q×B = m×v/r
then:
r = m×v/q×B
r = p/q×B
then, the kinetic energy of the proton:
K = 1/2×m×v^2 = p^2/(2×m)
q×B = \sqrt{2×m×K}/r
r = \sqrt{2×m×K}/(q×B)
= \sqrt{2×(1.67×10^-27)×(5.3×1.60×10^-13)}/(1.60×10^-19×0.39)
= 0.85 m
Answer:
that best describes the process is C
Explanation:
This problem is a calorimeter process where the heat given off by one body is equal to the heat absorbed by the other.
Heat absorbed by the smallest container
Q_c = m ce (
-T₀)
Heat released by the largest container is
Q_a = M ce (T_{i}-T_{f})
how
Q_c = Q_a
m (T_{f}-T₀) = M (T_{i} - T_{f})
Therefore, we see that the smaller container has less thermal energy and when placed in contact with the larger one, it absorbs part of the heat from it until the thermal energy of the two containers is the same.
Of the final statements, the one that best describes the process is C
since it talks about the thermal energy and the heat that is transferred in the process
