I'm trying to remember the title of a film in which a crew of very young people are embarked on a ship for a trip to a distant planet. There is almost no images of the planet until the end, when the youngest of them recovers a broken transmission. On their trip they get an older man (actually some sort of captain of a military ship) who helps them in a combat by crafting a cannon (they were sent unarmed). I remember two scenes that may be definitory:   In one scene one of the guys is weight training with just two small transparent pieces on his hands, whose weight is remotely adjusted. In another scene, the "bad guy" on the crew (the one who actually liked computer games more than studying and who barely graduated) saves the ship from an asteroid field by driving the ship as if it were a videogame. EDIT: Not actually asteroids but debris.   Can somebody remember which film was this? It is most probably from the 80's.  Thanks.
When I was a kid we had a VHS tape of some Disney live action (not animated) sci-fi movie. It may have been a mini-series or a made-for-tv movie, but I'm not sure. I'm also not sure about the year but it would probably have been late 80s or early 90s based on when I would have seen it. I know it was Disney because they had some live action Goofy and Mickey running around the movie's set as an introduction discussing the plot with a host before the movie.  The plot is basically as follows:   A starship is loaded with mostly children and teenagers as a cross-galaxy human settling effort. Accidents (which are not really accidents and later revealed) cause adult crew members to be killed.  They travel to another planet and face all sorts of troubles. It arrives at the new planet after overcoming obstacles.   Other memorable scenes that may help:   Navigating out of earth's asteroid belt made out of space junk. One of the adults was killed via an airlock malfunction. The ship was supposed to be peaceful with no weapons. At one point they bring on board some crazy guy who puts together a rail gun. There's a memorable line like "Do you want no weapons at all or a well aimed rock?"  There's a planet or space station (I can't remember which) that has a fight scene with the evil bad guy. This scene takes place on what looks to be a carnival or fairground. The bad guys are trying to steal the ship the kids are on because it has some kind of really good futuristic space drive.   Hopefully you remember it better than I do! I've tried looking online for it before with no luck.
iOS: Your passcode is required to enable Touch ID Occasionally, when unlocking my iPhone or iPad, I get the following message:     Your passcode is required to enable Touch ID   Now this is not after a number of failed attempts or turning the device off. The device was used within the last 12 hours. Two of the devices are less than 2 months old, and one is a year old. Everything is up to date. It appears to be happening more-or-less at random.  Does anybody know why this message might appear? Prove $n\mid \phi(2^n-1)$ If $2^p-1$ is a prime, (thus $p$ is a prime, too) then $p\mid 2^p-2=\phi(2^p-1).$  But I find $n\mid \phi(2^n-1)$ is always hold, no matter what $n$ is. Such as $4\mid \phi(2^4-1)=8.$  If we denote $a_n=\dfrac{\phi(2^n-1)}{n}$, then $a_n$ is , but how to prove it is always integer?  Thanks in advance! I think some good words would be conflicted, or confused. As an example of context, think of someone who believes in freedom of speech, but, at the same time, they would support banning comedians who make jokes about certain issues that person cares about. What is an example of a transformation on a posterior distribution such that the MAP estimate will be non-invariant? Suppose that we have a posterior distribution $p(\theta\mid y)$ and we wish to define a transformation on $\theta$ such that $\phi = f(\theta)$. I know that generally such transformations will not affect the MLE as it is on the data space, but will result in non-invariance on the Maximum A Posteriori (MAP) estimate as it is a function of the parameter space. I am wondering if there is an example to illustrate this? Thanks. Max dimension of a subspace of singular $n\times n$ matrices I am sure the answer to this is (kind of) well known. I've searched the web and the site for a proof and found nothing, and if this is a duplicate, I'm sorry.  The following question was given in a contest I took part. I had an approach but it didn't solve the problem.     Consider $V$ a linear subspace of the real vector space $\mathcal{M}_n(\Bbb{R})$ ($n\times n$ real entries matrices) such that $V$ contains only singular matrices (i.e matrices with determinant equal to $0$). What is the maximal dimension of $V$?   A quick guess would be $n^2-n$ since if we consider $W$ the set of $n\times n$ real matrices with last line equal to $0$ then this space has dimension $n^2-n$ and it is a linear space of singular matrices.  Now the only thing there is to prove is that if $V$ is a subspace of $\mathcal{M}_n(\Bbb{R})$ of dimension $k &gt; n^2-n$ then $V$ contains a non-singular matrix. The official proof was unsatisfactory for me, because it was a combinatorial one, and seemed to have few things in common with linear algebra. I was hoping for a pure linear algebra proof.  My approach was to search for a permutation matrix in $V$, but I used some 'false theorem' in between, which I am ashamed to post here. java swing background image Suppose $G$ is a semigroup and it holds both left and right cancellation. Suppose $G$ is a semigroup and it holds both left and right cancellation. Also for each $a,b\in G$, $xa=b$ has solution in $G$. Prove G is a group.   I know this question looks very "old" style. First I think it's easy for me too since I already practice probelems like "semigroup, $xa=b$ and $ax=b$ have solution , then group" Or "finite semigroup, both left and right cancellation hold, then group ". But I still get stuck... My try:  First of course, for $xa=a$ , there exists $e_a$ such that $e_aa=a$. Now we need to proof $e_a$ is left identity for all elements. Then left inverse exists hence $G$ is a group. But the key is to proof $e_ab=b$ for all $b\in G$. Selecting a Textbox Item in a Listbox does not change the selected item of the listbox What is the exact difference between an autoregressive (AR) and vector autoregressive model (VAR)?  I always thought that VAR would just be for more than two variables, until I learned that AR can also have more than two variables. I.e. I had a misunderstanding(?) that AR models are not always bivariate.  Before I write too much potentially false assumptions about the difference between AR and VAR, it would rather be interested to see if anyone can make provide a quick and good summary. From a toggle to an impulsion I'm trying to make a circuit (with no programmable circuits, only logic gates, flip flops and latches) that outputs a short impulsion each time it's input toggles from 0 to 1. Do you have any idea of how to do so? How to access object properties containing special characters? My Mac is getting really slow, what should I do? Difference between "the very first" and "first" I have the sentence:     Who wrote the very first dictionary ever?   Is it any different from     Who wrote the first dictionary ever?   I don't get how something could be more first. I dont know how to sort a list of SObject Case.  I have a List&lt;Case&gt; newCases which i iterate over in for cycle, where i save Cases to my new List&lt;Case&gt; casesList.  for (Case newCase : newCases) {             if(newCase.Case_Content__c == '111' &amp;&amp; newCase.Status == '24'){                 String cuid = newCase.CUID__c;                 cuidSet.add(cuid);                 casesList.add(newCase);                 casesList.sort(); //TODO sorting by CUID__c             }         }   What i need to do is, to sort this new list by field CUID__c. So the Cases with same CUID are together.  Thank you for any help :) UNITY : I want to make my UI text fade in after 5 seconds I know this question has been asked and asked but none of the topics i visited gave me an answer. I'm making a game programmed in c# where you control a boat and i want my UI to appear smoothly by fading in after X seconds. May someone help me? I'm trying to identify a song by a female 80's pop group.   Here are the lyrics I remember:     It's the story of my life if you want to know   a play where everything is meant to be   you're the story of my life and I can't let you go For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $ Suppose that $f$ is continous on $[0,1]$ , differentiable on $(0,1)$ , and $f(0)=0$ and  $f(1)=1$.For every integer $n$ show  that there must exist $n$ distinct points $\alpha_1,\alpha_2\cdots,\alpha_n$ in that interval so that    $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $   Is it theorem or i can show it with basic differentiation knowledge .Please give me hint . Can grep output only specified groupings that match? Say I have a file:  # file: 'test.txt' foobar bash 1 bash foobar happy foobar   I only want to know what words appear after "foobar", so I can use this regex:  "foobar \(\w\+\)"   The parenthesis indicate that I have a special interest in the word right after foobar.  But when I do a grep "foobar \(\w\+\)" test.txt, I get the entire lines that match the entire regex, rather than just "the word after foobar":  foobar bash 1 foobar happy   I would much prefer that the output of that command looked like this:  bash happy   Is there a way to tell grep to only output the items that match the grouping (or a specific grouping) in a regular expression? Why are PCA eigenvectors orthogonal and what is the relation to the PCA scores being uncorrelated? I'm reading up on PCA, and I'm understanding most of what's going on in terms of the derivation apart from the assumption that eigenvectors need to be orthogonal and how it relates to the projections (PCA scores) being uncorrelated? I have two explanations provided below which use a link between orthogonality and correlation but fail to really explain it: , .  In the second picture it says that the condition $a_{2}^{T}a_{1}=0$  is imposed to ensure that the projection $y_{2}=Xa_2$ will be uncorrelated with $y_{1}=Xa_1$. Can someone provide an example to show why orthogonal vectors ensure uncorrelated variables?  What would happen in PCA if I chose vectors which are not orthogonal; is this even possible? I have read elsewhere that orthogonality is just a by-product of the covariance matrix being symmetric which would suggest that it's not possible to have non pairwise orthogonal eigenvectors. However in the first picture in search of the most 'suitable' matrix it almost seems as we are choosing $p_{1},\ldots,p_{m}$ to be orthogonal to give us a more convenient matrix $\textbf{P}$ one which has nice properties.  I've read other posts on this topic but have been unsatisfied with incorporation of the intuition with uncorrelated variables. I really appreciate any help in understanding this confusion!! I want it to be look like this:    I have an HDD and an SSD in my PC, I want to install Ubuntu to SSD, I have windows on HDD. I want to be able to boot ubuntu from the windows 10 uefi boot manager. How do I do it?