How do I stop the jpeg picture from reverting to its original position landscape after I have rotated the picture and saved the document, then opened it again to find it has gone back to landscape ?

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Although @JohnHa is absolutely right telling you to always use native formats in any software to ensure correctness (which is what the warning shown when saving to non-native formats is about), still RTF is quite capable format, able to retain image rotation correctly. So, if LibreOffice fails do save rotated image in RTF correctly, it's a bug in LibreOffice.

Yet, I was unable to reproduce with Version: 6.4.1.1 (x64) Build ID: 56f3c78975db08733f771c53643b5d1aa7c57567 CPU threads: 12; OS: Windows 10.0 Build 18363; UI render: GL; VCL: win; Locale: ru-RU (ru_RU); UI-Language: en-US Calc: CL. Since you omitted the version you used, it could be a bug with some older version; or you could use some specific procedure (rotated 90° right? left? to some other degree?), which also wasn't described in detail.

So, first try with an up-to-date version; if the problem is reproduced there, please file a bug, and don't forget to describe the problem in detail. Attaching a sample ODT or RTF with an image to the bug, which you know would demonstrate the problem if follow the steps, would also be useful, even if you are sure that "any image in any file would do", since sometimes it's a specific configuration or an image format flavor, like produced by a specific scanner, or whatever, that might make difference.

Saving the document as a .rtf is almost certainly the reason. Did you read the warning LO gave that saving as a .rtf file may lose formfitting and content? Or have you switched off that warning?

.rtf files are truly awful and very limited in their capability. You should always save your files as .odt.