Q: To find a vector's components, it's usually necessary to know its magnitude and its direction relative to the horizontal or vertical and to have a working knowledge of trigonometry. Taking a 2-D vector first: set or imagine your vector as the hypotenuse of a right triangle whose other two sides are parallel to the x and y axes. These two sides can be thought of as head-to-tail component vectors that add to create your original vector.  The lengths of the two sides are equal to the magnitudes of the x and y components of your vector and may be calculated using trigonometry. If x is the magnitude of the vector, the side adjacent to the vector's angle (relative to the horizontal, vertical, etc.) angle is xcos(θ), while the side opposite is xsin(θ). It's also important to note the direction of your components. If the component points in the negative direction of one of your axes, it is given a negative sign. For example, in a 2-D plane, if a component points to the left or downwards, it is given a negative sign. For example, let's say that we have a vector with a magnitude of 3 and a direction of 135o relative to the horizontal. With this information, we can determine that its x component is 3cos(135) = -2.12 and its y component is 3sin(135) = 2.12 When you've found the components of all of your vectors, simply add their magnitudes together to find the components of your resultant vector. First, add all the magnitudes of the horizontal components (those parallel to the x-axis) together. Separately, add all the magnitudes of the vertical components (those parallel to the y-axis). If a component has a negative sign (-), its magnitude is subtracted, rather than added. The answers you obtain are the components of your resultant vector. For instance, let's say that our vector from the previous step, <-2.12, 2.12>, is being added to the vector <5.78, -9>. In this case, our resultant vector would be <-2.12+5.78, 2.12-9>, or <3.66, -6.88>. The Pythagorean Theorem, c2=a2+b2, solves for the side lengths of right triangles. Since the triangle formed by our resultant vector and its components is a right triangle, we can use it to find our vector's length and therefore its magnitude. With c as the magnitude of the resultant vector, which you're solving for, set a as the magnitude of its x component and b as the magnitude of its y components. Solve with algebra. To find the magnitude of the vector whose components we found in the previous step, <3.66, -6.88>, let's use the Pythagorean Theorem. Solve as follows:  c2=(3.66)2+(-6.88)2  c2=13.40+47.33 c=√60.73 = 7.79 Finally, find the resultant vector's direction. Use the formula θ=tan-1(b/a), where θ is the angle that the resultant makes with the x-axis or the horizontal, b is the magnitude of the y component, and a is the magnitude of the x component. To find the direction of our example vector, let's use θ=tan-1(b/a).  θ=tan-1(-6.88/3.66) θ=tan-1(-1.88) θ=-61.99o As noted above, vectors are defined by their magnitude and direction. Be sure to use the proper units for your vector's magnitude. For example, if our example vector represented a force (in Newtons), then we might write it as "a force of 7.79 N at -61.99o to the horizontal".
A: Use trigonometry to find a vector's components. Add or subtract two or more vectors' corresponding components. Calculate the magnitude of the resultant vector using the Pythagorean Theorem. Calculate the direction of the resultant with the tangent function. Represent your resultant vector via its magnitude and direction.

Q: In some states, you can withhold rent from a landlord who does not make necessary repairs. The repairs can’t be for minor things, like small cracks in the walls or missing linoleum or tile. Instead, the danger should be a substantial and serious threat to your health and safety. For example, if no heat is being provided during winter, then you have a serious threat. Typically, state law requires that you give the landlord sufficient time to make repairs before withholding rent. Accordingly, you should send written notice to your landlord that repairs are needed.  Be specific about the problem in the apartment. Also explicitly request that the landlord repair the problem as soon as possible. Be sure to type up a letter and mail it, preferably certified mail, return receipt requested. Hold onto the receipt as it serves as proof that your landlord received the notice. Your landlord generally gets a “reasonable” amount of time to make repairs. If the violation is more serious, then the landlord should correct the problem promptly. Typically, if the landlord hasn’t acted within 30 days, then you don’t have to wait any longer. Instead, you should stop into your courthouse and ask about creating a “rent escrow.” With a rent escrow, you would not pay your rent to the landlord. Instead, you pay it into the escrow, where it accumulates until the landlord actually makes necessary repairs. If you can create a rent escrow in your county, then the clerk should give you the form to complete. The form might be called an “Application and Affidavit for Tenant Rent Escrow,” “Petition in Action of Rent Escrow,” or some other title. Be sure to enter the information neatly, using black ink or a typewriter. In some counties, you can download the form and type in the information directly. Although each form will differ, you generally will be asked the following:  your name and address your landlord’s name and address the amount of your rent the conditions on the property that are hazardous the date you notified your landlord of the hazard that you request the creation of a rent escrow your signature You have to give the landlord notice that you are trying to create a rent escrow. Accordingly, you will need to serve notice on your landlord. Generally, you can serve notice by having someone deliver a copy of your petition and also a “summons,” which is a legal document you can get from the court clerk. Ask the clerk about acceptable methods of service. Before the judge will create the escrow account, you will need to attend a hearing. You will have to explain why you want to withhold rent and create the escrow. Be sure to bring any evidence that you have:  a witness who can testify as to the hazardous condition photographs or video of the hazard a copy of your notice to your landlord If the judge creates the escrow account, then you will need to regularly pay your rent into it. Be sure to make your payments, since the judge might close the escrow if you forget to.  The judge may order that some or all of the money in the escrow be given to the landlord to help pay for the repairs. If the landlord still refuses to make repairs, then all of the money in the escrow could be returned to you.
A:
Identify repairs that need to be made. Notify your landlord of the hazard. Wait a certain amount of time. Get a form from the court clerk. Complete the petition form. Serve notice of the action on the landlord. Attend a hearing. Pay rent into the escrow account.