Auto login to SSH without keys?
Shell Script for logging into a ssh server
Projectile/orbital motion over very long distance We know the optimum angle for greatest horizontal displacement when launching an object with projectile motion is 45 degrees.  How to solve the angle when it is real long distance around the earth where we cannot assume that gravity is constant but is given by $F=\frac {-GMm}{r^2}$. I use differetial equation to solve it and obtain 45 degrees.   First, for the vertical distance $y$, change $v=u-gt$ to $y'=u-y''t$. Then solve it to obtain a function $y(t)$. When $y'(t)=0$ we have the time for maximum vertical distance. Then insert the value to horizontal equation.   Can anyone guide me through this problem because I am not confident with my working Galaxy S not detected, how do I make it work? Can anyone please provide the necessary steps to connect a Samsung Galaxy S with Ubuntu 10.10 please? I was thinking that perhaps it could detect something, but it doesn't, Anyone succeeded ?   Thanks Edit Mode buttons for selecting vertices and edges vanished When I am in Edit Mode for my project, the Mesh Select Mode buttons have disappeared!  I loaded the default project and the buttons are where they are supposed to be; the issue is only in my project. From all the hard drives I have bought, they never seem to be as large as the advertised size; from 320 GB down to 290 GB, from 500 GB down to 450 GB, etc. Is there a technical reason for this? What intuitively is "bias"? I'm struggling to grasp the concept of bias in the context of linear regression analysis.    What is the mathematical definition of bias? What exactly is biased and why/how? Illustrative example? Is there anything canon in the Terminator Universe that picks up where Terminator: The Sarah Connors Chronicles leaves off? So, Terminator canon is pretty twisted, given all that time-travel stuff.  But in the canon that includes the T:SCC, does anything pick up where the show left off that is considered canon? Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove $\operatorname{trace}(A) = \operatorname{trace}(B)$.  I'm not sure where to go on this. So far I have this:  If $A$ is similar to $B$, then      $B=P^{-1}AP$ and $A=PBP^{-1}$   This implies that:     $\operatorname{trace}(B) = \operatorname{trace}(P^{-1}AP)$ and $\operatorname{trace}(A) = \operatorname{trace}(PBP^{-1})$   Not sure where to go from here Structure of groups of order $pq$, where $p,q$ are distinct primes. I don't know about the Sylow Theorems.  But I have been wondering about a proof of the fact that a group or order $pq$ where $p$ and $q$ are distinct primes must be cyclic. I can't quite work out the details, but here is the general idea. I would like help with filling in details. I assume that it is already known that $G$ has subgroup(s) of order $p$ and subgroup(s) of order $q$.  If $G$ is a group of order $pq$ ($p\neq q$), then I know that $G$ has a subgroup $H$ of order $p$ and a subgroup $K$ of order $q$. Then $H\simeq \mathbb{Z}_p$ and $K\simeq \mathbb{Z}_q$.   But then $H\oplus K \simeq \mathbb{Z}_{pq}$, so I would think that $H\oplus K \simeq G$. I guess one could do an internal direct product instead of an external direct product, but I don't know that $H$ and $K$ are normal subgroups.  I am asking for help completing this argument.  Edit: I see from the comments below that I might need to assume that the smaller prime does not divide the larger prime minus $1$. Or maybe it is enough to assume that the primes are greater than or equal to $3$ (Still distinct). What's the difference between Kage Bunshin no Jutsu and Tajuu Kage Bunshin no Jutsu? While the Kage Bunshin no Jutsu seems to be taught, the Tajuu Kage Bunshin no Jutsu is sealed, so nobody can learn the jutsu. Does that mean that there's a difference between these jutsus, aside from the number of Kage Bunshin created?   Or, why was the Tajuu Kage Bunshin no Jutsu sealed away? If there's no other difference, everybody could use this without reading the sealed scroll. Flash Player works on Firefox, but not on Chromium? I want to play online games, and other online stuff that requires Flash Player on the internet. Flash Player works just fine under Firefox, but in Chromium I just get a blank page. I don't know what is the exact problem or know to fix it. Landscape figure in LaTeX I have a figure I'm trying to insert which is in landscape and I'm using the following (snipped) code:  \documentclass[12pt, oneside]{book} \usepackage{graphicx} \usepackage{wrapfig} \usepackage{lscape} \usepackage{rotating} \usepackage{epstopdf}  \begin{document}  \begin{figure}[ht]     \includegraphics{../figures/pics/DivLibPropProfile}     \caption{Property profile of the diverse library compared to the compound pool.}     \label{fig:PropProf} \end{figure}  \end{document}   When I compile this with pdfLaTeX the output behaves as I'd expect – page in portrait with the caption at the bottom but the figure in the "wrong" orientation.  However when I compile using LaTeX, the page is turned landscape with the figure now in the correct orientation but with the caption at what is now the left of the page rather than under the figure, which you should get using \begin{landscape}.    When I do use the landscape environment and compile with LaTeX the caption the whole page is turned upside-down and everything is wrong.  Any ideas how I can get the correct orientation of landscape figure on landscape page with the caption under the  (attached for reference)?  I also need to use LaTeX rather that pdfLaTeX for another package to function. Multiplicative inverse questions This is my first time posting on Math exchange. I have been self-teaching myself Mathematics and recently started learning some Algebra. I was posed the following questions, in which I would like to answer before I proceed, but having some trouble finding proper solutions. So the format will be question, and my answer.      What name do we give an element $a \in \mathbb{Z}_n$ that has a multiplicative inverse?   A modular multiplicative inverse of an integer $a$ is an integer $x$ such that $ax \cong 1 (\mod m)$. This means that the remainder after dividing $ax$ by integer $m$ is equal to $1$.      Give an example, for some $n \in \mathbb{N}$, of an element of $\mathbb{Z}_n$, that does not have a multiplicative inverse?   This question is throwing me off because - does the $n$ we speak of matter for both $n \in \mathbb{N}$ and $\mathbb{Z}_n$ ot solely $n$? My guess here would be $0$ because we cannot have an inverse of $0$.      Prove that multiplicative inverse are unique; an element $a \in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Suppose that an element $a\in\mathbb{Z}_n$ has an inverse $a'$. Next, suppose that $a^*$ is also an inverse of $a$. Then, $a'$ is a solution to $a \cdot_n x=1$, and similarly $a^*$ has a solution to $a \cdot_n x=1$.   Lemma: Suppose $a'$ is multiplicative inverse of $a$ in $\mathbb{Z}_n$, then for any $b \in \mathbb{Z}_n$ the equation $a \cdot_n x=b$ has a unique solution, such that $x = a' \cdot_n b$.   By Lemma, equation $a \cdot_n x = 1$ has a unique solution, namely $x=a'=a^*$. Therefore, an element $a\in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Thank you for the help. I would love any constructive feedback for these. If you can help me elaborate on some ideas, that would be really helpful also.  Thank you very much! Beamer, page/frame numbers, buttons and Appendix slides Geometric interpretation of Electromagnetism For gravity, we have    General Relativity, which is a geometric theory for gravitation.  Is there a similar analog for Electromagnetism? A groupoid is defined to be a category where every morphism is an isomorphism. So sometimes a group is said to just be a groupoid with one object.   When I try to make sense of this, I denote the single object as $G$. I view the morphisms as the analogue of "elements." The identity $1_G$ is the analogue of the usual identity $e$, we can compose any two morphisms since they are all arrows on $G$, and for any arrow $f$, we have some $f^{-1}$ such that $f\circ f^{-1}=f^{-1}\circ f=1_G$, so the idea of inverses is still there.  So I informally associate the elements of the group in the usual definition to be the arrows in the groupoid. But what does the sole object $G$ in the groupoid "correspond to" if I were to try to informally make sense of a group in the usual sense? Does it even correspond to anything? How do you get vim to display wrapped lines without inserting newlines? I'm getting back in touch with my inner (g)vim due to an unscheduled MacBook mother(board) of a meltdown (my emergency backup Linux box won't run TextMate). All told I'm happy with vim's efficiency and power, but I'm mortified at how hard it is to get the kind of word wrap that even stupid HTML textareas achieve with no apparent effort.  Consider the text  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nullam.  By default, with an 80-character width vim displays this as  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nu llam.  This wrapping doesn't care about whitespace, so sometimes it just slices words into pieces (nullam in this case). Of course, you can turn on word wrap, and get this:  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nullam.  The problem is that vim inserts a newline at the linebreak, which I most emphatically do not want. In other words, I want the text to display exactly as vim displays it with word wrap turned on, but without inserting a newline. (This way it can be pasted into HTML textareas and email programs, among other places.)  Web searches have yielded nothing of use, despite diligent effort; I hope StackOverflow can succeed where my Google-fu has failed. How do I upgrade to a newer version of Ubuntu? What are the different ways I can use to upgrade Ubuntu from one release to another? Show that if $n$, $a$, $b$, and $c$ are positive integers with $\gcd(a, b) = 1$ and $ab = c^n$, then there are positive integers $d$, and $e$ such that $a = d^n$ and $b = e^n$.   I know that (by Bezout) $\gcd\left(a,b\right) = 1$ implies $ax + by = 1$ for some integers $x$ and $y$, and also that $\gcd\left(a^n,b^n\right) = 1$, but this does not help me. Dimensioning of a technical drawing in TikZ Is there is an easy way to mark dimensions in a technical drawing with TikZ?    Is there a library or something?  Edit  I am using XeLaTeX.  Update  I chose Martin's answer because it serves me well for the moment. Ultimately the best solution would be a library that, in an easy and consistent manner, would allow to change the arrow/dimension lines styles, would support polar coordinates, would allow to choose 2 nodes and the vertical distance that you want the dimension to be typeseted etc. After Google Play Service update to version 13 I got an error