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Just about every work I've read on air acoustics (I've read a lot) starts by assuming constant sonic velocity. I sort of understand the reasons for this, but it simply isn't accurate. The peak of the pressure wave is hotter and the trough cooler due to compression/expansion and this does affect sonic velocity. I believe it's significant enough to be a major factor in eg. developing the characteristic timbres of wind instruments which nobody seems to have got a proper theoretical handle on yet. I've made a start on developing a mathematical system modelling a spherical wave accommodating a variable sonic velocity and attached a brief summary. I'd be most grateful if someone would give it a quick once over to see if I've made any blunders along the way. The pair of simultaneous ODEs I've come up with are beyond my skills to solve analytically, but they're quite amenable to numerical integration. Any hints from the more mathematically gifted would also be much appreciated. Spherical Adiabatic Acoustics.pdf

This seems to be one of those points where you think something is going on, some kind of deceit or exaggeration or stubborn willfulness. You seem to think people with different mindsets regarding gender and sexuality are simply acting on a whim, making non-typical decisions simply to be contrary, or overly demanding, or because it strikes their fancy. "Whatever they please without consideration or consequence" is what you claim, as if you actually knew the mindset of folks like this. Be careful that you aren't misattributing motives. Many people think LGBTQ folks choose to be this way so they can get around the system (to be in a different bathroom or dressing room, for instance). What if it's not a choice, and acknowledging the truth of it was always the primary concern, and things like where to go to the bathroom or change your clothes didn't even cross their minds till later?

Historically, the same mindset was applied to homosexuality. Nobody is identifying as a dog, but you raise a valid point that people’s rights shouldn’t be limited when/if they do. “Gay marriage?!? What’s next… letting people marry their dog!!” Ahh… memories.

Excuse me, but old? What the heck, man? Totally uncalled for.

Especially as these issues have nothing to do with other. Legally it is a bit of grey zone as many countries do not seem to have laws explicitly prohibiting marriages with animals. The wiki article is a bit of a mess https://en.wikipedia.org/wiki/Human–animal_marriage. But I think these lines of argument follow a rather similar structure. First, remove any reasonable context (there are no laws explicitly forbidding human animal marriages as these things are normally expected to happen, same as marriages with plants, rocks or bodies of water are prohibited) and then cram in something you don't like (homosexuality, transgenderism, poets). Thereby it is easy to create ridiculous scenario to attack. I mean, clearly poets are linguistic deviants who just want to disassemble clear communication. All these contortions using rhymes and unusual sentence structures rob us of our ability to clearly present facts. As such, they should be banned under law. After all, what prevents me to declare myself a science poet and force journals to publish my gibberish!

So, answering the actual, actual question😃, since MW of CaCO3 is 40+12 + (16x3) = 100, 2g would absorb 2/100 x 177.8 = 3.556kJ, wouldn't it?

It's not the wheel that's the problem, it's the axle.

To put it mathematically If LT represents a Lorentz transformation is represents a transformation of something. That something is one of the four coordinates, x,y,z,t. It is easy to show that aLT (x) = LT (ax) ; where a is some coefficient. and the same for the other three coordinates. As joigus noted, LT does not act directly on v, the relative velocity. which is a condition that forms part of the definition of linear in mathematics.

If U is a 4-vector, then the formula for a Lorentz transformation from the original frame to some primed frame is written as \[U’=\Lambda(v)U\] where \(\Lambda\) is a square matrix, the Lorentz transformation matrix, and v is some parameter of the transformation (not necessarily speed!). I invite you to verify yourself that \[\Lambda(v+u)=\Lambda(v)+\Lambda(u)\] and (c=const.) \[\Lambda(cv)=c\Lambda(v)\] by whatever means you find most convenient. The above two relations define the property of linearity in the context of matrix transformations. So yes, the Lorentz transformations are indeed very much linear - as of course they have to be, since they map lines into lines, ie inertial frames into inertial frames. This is pretty trivial tbh. P.S. Cross posted with joigus, studiot and Grenady! Had my reply open on screen some time before hitting “Submit”.

The transformations are linear. The formulae involved are not. Edit since composing this I see a non productive exchange of red points.

Because the principles that govern their behavior are independent of their histories (according to SR). Don't be silly. [math]\gamma[/math] is nonlinear in the velocity.

They are linear.

That might be tried by a single person. Not sure. This a list of all occasions requiring multiple ballots. https://history.house.gov/People/Office/Speakers-Multiple-Ballots/

Aren't you lucky, not to be conflicted about your sexuality.

Anyone else notice Toucana always posts OPs like this on political topics, doesn’t frame the discussion, then also never really engages? Anyway… Now it’s 11. The House has adjourned and McCarthy has lost 11 votes for Speaker.

Here is a maths free resource for those looking for Maths Tutorials, from the Centre for Innovation in Maths Learning. The two links give the centre's home page, a topic list. https://www.cimt.org.uk/ https://www.cimt.org.uk/projects/mepres/alevel/ These are first class resources available for download in pdf.

From a thread: To clarify a few things- The main purpose of the rule is to prevent thread-starters from just posting a link to their site and having that be their contribution to the discussion. This would invite spammy behavior, which we want to discourage. We don’t like links to commercial sites, but that’s primarily sites that are selling things. We are also wary of people repeatedly linking to a particular site, i.e. they are driving traffic there. (i.e. don’t post just to link to Bob’s news aggregator or blog) It’s OK to post links to sites that have info helpful to a discussion. If there is a particularly relevant passage, we encourage you to quote it as well. If you are rebutting a claim, then this is necessary to focus the conversation; it’s not reasonable to force people to sift through a link to get the important information. In this case, the thread was in science news. Posting news links there is not only allowed, it’s expected.