Find all instances on a 24 hour analog clock where if the hour and minute hands are interchanged we get a valid time.    Solution:  Let the position of the hour and minute hands be measured clockwise in degrees from the vertical.  Let:       X  =  position of hour hand    24X  =  position of minute hand  (mod 360)     After interchanging the hour and minute hands:    24X  =  position of hour hand    (mod 360)    576X  =  position of minute hand  (mod 360)  =  X    We seek all solutions to:       X  =  576X (mod 360)       0  =  575X (mod 360)       X  =  (360/575)N; N  =  0, 1, 2, …, 574
At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and the minute hand position does a clock still give a valid time?
Extrude Faces along Local Normals I am trying to extrude faces of a cylinder along local normals. 3dsmax can do it easy, couldn't find how to do it in blender.  The extrude region option extrudes it as shown in the first example. I want it done like the 2nd example. My Y axis is inverted! How do I fix that? When I play Black Ops 2, it seems that my xbox controller is inverted. Example: if I press up, my character looks down and vice versa. It was not like this before. Does anyone know how to reset the controller back to its original settings? I've seen a lot of times the pronoun them used like an article. For example, in the title of the Delta Rhythm Boys Them bones, or in the first sentence of "Money for nothing":     Now look at them yo-yo's, that's the way you do it.   I know that it's not "proper English" (i.e., not something you'll use in a serious writing), but I'd like to know when it's commonly used, and why. Is there any difference between using it and using the? Do the SSH or FTP protocols tell the server to which domain I am trying to connect? When using the ssh or ftp commands from the Bash shell, does the server that I am connecting to learn of the domain name used? I understand that the domain name is locally translated into an IP address via DNS. In HTTP, after that happens, the server is told the original domain name as well in order to serve the correct page, or to present the correct TLS cert (SNI).  host serverfault.com GET /   Does a similar phenomenon happen when connecting to ssh or ftp?  I ask because I am  trying to ssh into a server (GoDaddy webhosting) which expects a domain name, but is not letting me in when I try to connect via user@IPaddress as the DNS is not yet moved to the GoDaddy IP address. If I want to print multiple figures in figure, I'm using subfigure in the figure environment. This work quit well and is looking smart, if all figures have the similar height. Now there is this figure which is more than two times higher than the other ones. I would like to order the subfigures like its shown in the following picture:     But I don’t know how to get this into Latex.   My regular code for four subfigures:  \begin{figure} \centering \begin{subfigure}{0.32\textwidth}    \centering    \includegraphics[width=\textwidth]{highone}    \caption{}    \label{fig:a} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{b}     \caption{}     \label{fig:b} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{c}     \caption{}     \label{c} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{d}     \caption{}     \label{fig:d} \end{subfigure} \caption{Blabla.} \label{fig:abcd} \end{figure}   Thank you for your help! Generating correlated binomial random variables I was wondering if it might be possible to generate correlated random binomial variables following a linear transformation approach?  Below, I tried something simple in R and it produces some correlation. But I was wondering if there is a principled way to do this?  X1 = rbinom(1e4, 6, .5) ; X2 = rbinom(1e4, 6, .5) ;  X3 = rbinom(1e4, 6, .5) ; a = .5  Y1 = X1 + (a*X2) ; Y2 = X2 + (a*X3) ## Y1 and Y2 are supposed to be correlated  cor(Y1, Y2) Prove that a function is not injective Show that the condition number of an invertible matrix must be at least 1. What matrices have  condition number equal to 1.  If someone could help me with this and give an explanation that would be very helpful. I do not know where to start How to start a new Linux distro? I want to transfer my current system hard drive to a larger hard drive. Doing so, I thought of creating an image of my system hard drive which is 320 GB in size.   Would I be able to restore this image on a larger hard drive? I plan buying a 1TB hard drive.  If yes, how? I prefer no data loss.  I am using Windows 7 Enum ToString with user friendly strings My enum consists of the following values:  private enum PublishStatusses{     NotCompleted,     Completed,     Error };   I want to be able to output these values in a user friendly way though. I don't need to be able to go from string to value again. Integration of secant $$\begin{align} \int \sec x \, dx  &amp;= \int \cos x \left(  \frac{1}{\cos^2x} \right)  \, dx \\ &amp;= \int \cos x \left(  \frac{1}{1-\sin^2x} \right) \, dx \\ &amp; = \int\cos x\cdot\frac{1}{1-\frac{1-\cos2x}{2}} \, dx \\ &amp;= \int \cos x \cdot\frac{2}{1+\cos2x} \, dx  \end{align}$$  I am stuck in here. Any help to integrate secant? Creating Inky-looking characters in Blender Server 2008 Net Send or Msg? I have a Windows 2008 server running as a domain controller. The details are as follows:  Domain: corp Server Name: oxygen   The workstations are all running Windows XP SP3 and have fixed IP addresses.  I am trying to use the net send functionality to be able to send simple messages to either individual machines/users and also to all machines. This is so I can send a message to a user to alert them about something, or likewise alert everyone of something such as the server being rebooted.  Is this possible using Windows Server 2008? If so, what would the command be? Do I make money in the stock market from other people losing money? Here is my player code.  Rigidbody rb;  Vector3 currMovement; public float jumpSpeed = 10; public float moveSpeed = 10; public float rotSpeed = 180;  float distToGround;  public float posSmoothTime = 0.5f; float currPos; float targetPos; float posVel;  public float rotSmoothTime = 0.5f; float currRot; float targetRot; float rotVel;  void Start() {     rb = GetComponent&lt;Rigidbody&gt;();     distToGround = GetComponent&lt;Collider&gt;().bounds.extents.y; }  bool isGrounded() { return Physics.Raycast(transform.position, Vector3.down, distToGround + 0.1f); }  void Update() {     Move(); }  void Move() {     // Rotation smoothing.     targetRot = Input.GetAxisRaw("Horizontal") * rotSpeed * Time.smoothDeltaTime;      if (targetRot &gt; 360)         targetRot -= 360;     if (targetRot &lt; 0)         targetRot += 360;     currRot = Mathf.SmoothDampAngle(currRot, targetRot, ref rotVel, rotSmoothTime * Time.smoothDeltaTime);      transform.eulerAngles += new Vector3(0, currRot, 0);      // Movement smoothing.     targetPos = Input.GetAxisRaw("Vertical") * moveSpeed;      currPos = Mathf.SmoothDamp(currPos, targetPos, ref posVel, posSmoothTime * Time.smoothDeltaTime);     currMovement = new Vector3(0, 0, currPos);     currMovement = transform.rotation * currMovement;      if (isGrounded())     {         if (Input.GetButtonDown("Jump"))             rb.velocity += Vector3.up * jumpSpeed;     }      rb.position += currMovement * Time.smoothDeltaTime; }   I have a Rigidbody attached to my player. I think the problem is with my camera script. Here is my camera script.  public Transform player; Quaternion targetLook; Vector3 targetMove; public float smoothLook = 0.5f; public float smoothMove = 0.5f; public float distFromPlayer = 5, heightFromPlayer = 3; Vector3 moveVel;  void LateUpdate() {     CameraMove(); }  void CameraMove() {     targetMove = player.position + (player.rotation * new Vector3(0, heightFromPlayer, -distFromPlayer));     transform.position = Vector3.SmoothDamp(transform.position, targetMove, ref moveVel, smoothMove);      targetLook = Quaternion.LookRotation(player.position - transform.position);     transform.rotation = Quaternion.Slerp(transform.rotation, targetLook, smoothLook); }   }  The player is not an parent of my camera. When I parent the player to my camera the shake stops. But I want a custom smooth camera movement with my custom scirpt, so I can't make the player a parent of the camera. The reference to entity "foo" must end with the ';' delimiter Why don't digital cameras shoot video at full sensor resolution, or do continuous drive at video framerates? SQL Server: Examples of PIVOTing String data Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$ Let $z_1$ and $z_2$ be two complex numbers. Show that there exists $C &gt; 0$ with   $$  |z_1 + z_2|^2 &lt; (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2. $$   I tried to simplify the L.H.S and R.H.S, SNF I was finally left to compare between a real number and a complex number  I really couldn't think of anything else. Please help.